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165 LearnersLast updated on November 30th, 2024
LCM of 14 and 21
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
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.