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Last updated on November 30th, 2024

LCM of 14 and 21

Q: What is the relationship between the Greatest Common Divisor (GCD) and LCM of 14 and 21?

The relationship between GCD and LCM is expressed by the formula: LCM(a, b)×HCF(a, b)=a×b Verifying this, LCM (14,21)×HCF (14,21) 42×7=14×21 —> 294=294 This formula shows how the GCD and LCM complement each other.

Q: What is the LCM of algebraic expressions?

For algebraic expressions, find the LCM by factoring each expression and then choosing the highest power of each variable. For example ; Find the LCM of x2y and xy3 Factor each term as follows x2y = x2 × y —---> the highest power = x2 xy3 = x × y3 —---> the highest power = y3 Multiply the highest powers —---> x2y3 LCM(x2y, xy3) = x2y3

Q: How do you find the LCM with different bases in an exponential equation?

You can find the LCM For exponential equations with different bases by following the below example, Find the LCM of 144×212 and 213×143 Factorize the terms and find the highest power Highest power of 14 = 144 Highest power of 21= 213 LCM = 144×213

Q: What is the LCM formula using the HCF ?

The LCM can be found using the formula: LCM (a, b)= a×b/HCF(a, b) For 14 and 21, HCF(14,21)= 7 So, LCM(14,21)=14×21/7 = 42

Q: How do you derive the LCM of two decimal numbers? Explain using 14.0 and 21.0.

To derive the LCM of two decimal numbers, follow the below steps; First, convert the given decimals to whole numbers. In the given case, 14.0 and 21.0 are already whole. However, if there is a case where the decimal is, say, 4.5, multiply it by 10 to convert them to a whole number, which will be 45. After converting them into whole numbers, ascertain the LCM of the digits using any of the methods, i.e., the listing multiples method, the division method or the prime factorization method. The LCM (14,21)= 42

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 14 and 21. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

What is the LCM of 14 and 21?

The LCM of 14 and 21 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.

How to find the LCM of 14 and 21?

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;

LCM of 14 and 21 using the Listing multiples method

To ascertain the LCM, list the multiples of the integers until a common multiple is found.

Steps:

1. Write down the multiples of each number:

Multiples of 14 = 14,28,42,…

Multiples of 21= 21,42,63…

2. Ascertain the smallest multiple from the listed multiples

The least common multiple of the numbers is 42.

LCM of 14 and 21 using the Prime Factorization

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.

Steps:

1. Find the prime factors of the numbers:

Prime factorization of 14 = 2×7

Prime factorization of 21= 3×7

2. Take the highest power of each prime factor and multiply the ascertained factors.

— LCM = 42

LCM of 14 and 21 using the Division Method

The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.

Steps:

1. Write down the numbers in a row;

2. Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.

3. The LCM of the numbers is the product of the prime numbers in the first column, i.e,

2×7×3 = 42

Common Mistakes and how to avoid them while finding the LCM of 14 and 21

LCM of 14 and 21 Examples

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

Ram goes to the office canteen every 14 days, and his boss goes every 21 days. After how many days will they meet on the same day again?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Explanation

Problem 2

Machine X stops for maintenance every 14 hours, while machine Y stops every 21 hours. In how long will the machines stop again?

Explanation

Problem 3

A store receives shipments of apples every 14 days and pineapples every 21 days. If both shipments arrive today, in how many days will both shipments arrive again on the same day?

Explanation

Problem 4

Leo, and Will, have classroom clean-up duties. Emma is assigned to cleaning duties every 14 days and Jack every 21 days. If both are assigned clean-up today, when will they next be assigned on the same day?

Explanation

FAQ’s on LCM of 14 and 21

1.What is the relationship between the Greatest Common Divisor (GCD) and LCM of 14 and 21?

2.What is the LCM of algebraic expressions?

3.How do you find the LCM with different bases in an exponential equation?

4.What is the LCM formula using the HCF ?

5.How do you derive the LCM of two decimal numbers? Explain using 14.0 and 21.0.

Important glossaries on the LCM of 14 and 21

Multiple: A product of a number and any integer.
Prime Factor: A prime factor is a natural number, other than 1, whose only factors are 1 and itself.
Prime Factorization: The process of breaking down a number into its prime factors.
Co-prime numbers: A number is co-prime when the only positive integer that is a divisor of them both is 1.
Greatest Common Divisor (GCD): The largest positive integer that divides each of two or more integers without leaving a remainder.
Relatively Prime Numbers: Two numbers that have no common factors other than 1.
Fraction: A number representing a part of a whole.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.