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Last updated on November 29th, 2024

LCM of 6 and 10

Q: What is the relationship between the Greatest Common Divisor (GCD) and LCM of 6 and 10?

The relationship between GCD and LCM is expressed by the formula: LCM(a, b)×HCF(a, b)=a×b Verifying this, LCM(6,10)×HCF(6,10) 30×2=6×10 —> 60=60 This formula shows how the GCD and LCM complement each other

Q: How does one know when to use LCM instead of HCF? Explain using the digits 6 and 10.

HCF is used while simplifying ratios or fractions, while, the LCM is used to find the solution for problems where a common time or event is required to be derived between two repeating cycles. In the given case of 6 and 10, the HCF (2) is used to simplify the operations. The smallest value to which 6 and 10 can be divisible into is 3 and 5 respectively. The LCM (30) is used to find the smallest common time/event between the digits, as explained in the examples above.

Q: What is the LCM of 6 and 10. Find it using the HCF?

The LCM can be found using the formula: LCM (a, b)= a×b/HCF(a, b) For 6 and 10, HCF(8,12)= 2 So, LCM(6,10)=6×10/2 = 30

Q: How do you derive the LCM of two decimal numbers? Explain using 6.0 and 10.0?

To derive the LCM of two decimal numbers, follow the below steps; First, convert the given decimals to whole numbers. In the given case, 6.0 and 10.0 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 (6,10)= 30.

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The Least common multiple (LCM) is the smallest number that is divisible by the numbers 6 and 10. 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 6 and 10?

The LCM of 6 and 10 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 6 and 10?

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

LCM of 6 and 10 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 6 = 6,12,18,24,30,…

Multiples of 10 = 10,20,30,40…

2. Ascertain the smallest multiple from the listed multiples

The least common multiple of the numbers is 30.

LCM of 6 and 10 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 6 = 2×3

Prime factorization of 10= 2×5

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

— 2,3,5 = LCM, i.e, 30

LCM of 6 and 10 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.

3. 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.

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

2×5×3 = 30

Common Mistakes and how to avoid them while finding the LCM of 6 and 10

LCM of 6 and 10 Examples

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Problem 1

Ram goes to the office every 6 days, and his boss comes every 10 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 6 hours, while machine Y stops every 10 hours. In how long will the machines stop again?

Explanation

Problem 3

A store receives shipments of apples every 6 days and bananas every 10 days. If both shipments arrive today, in how many days will both shipments arrive again on the same day?

Explanation

Problem 4

Emma and Jack, have classroom clean-up duties. Emma is assigned to cleaning duties every 6 days and Jack every 10 days. If both are assigned clean-up today, when will they next be assigned on the same day?

Explanation

FAQ’s on LCM of 6 and 10

1.What is the relationship between the Greatest Common Divisor (GCD) and LCM of 6 and 10?

2.How does one know when to use LCM instead of HCF? Explain using the digits 6 and 10.

3.What is the LCM of 6 and 10. Find it using the HCF?

4.How do you derive the LCM of two decimal numbers? Explain using 6.0 and 10.0?

Important glossaries for LCM of 6 and 10

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.