208 LearnersLast updated on May 26th, 2025
LCM of 6 and 7
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 6 and 7. 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 7?
The LCM of 6 and 7 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 7?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 6 and 7 using the Listing Multiples Method
The LCM of 6 and 7 can be found using the following steps:
Step 1: Write down the multiples of each number
Multiples of 6 = 6,12,…42,…
Multiples of 7 = 7,14,…42,…
Step 2: Ascertain the smallest common multiple from the listed multiples
The smallest common multiple is 42
Thus, LCM(6, 7) = 42.
LCM of 6 and 7 using the Prime Factorization Method
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Step 1: Find the prime factors of the numbers:
Prime factorization of 6 = 2×3
Prime factorization of 7 = 7
Step 2: Take the highest powers of each prime factor:
Highest power of prime factors= 2,3
Highest power of prime factor = 7
Step 3: Multiply the highest powers to get the LCM:
LCM(6, 7) = 2 ×3 × 7= 42
Thus, LCM(6, 7) = 42.
LCM of 6 and 7 using the Division Method
This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.
Step 1: Write the numbers, divide by common prime factors and multiply the divisors.
Step 2: A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of 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.
Step 3: 2× 3 × 7= 42
Thus, LCM(6, 7) = 42.
Common Mistakes and how to avoid them in LCM of 6 and 7
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 6 and 7, make a note while practicing.
Mistake 1
Recognizing that numbers 6 and 7 are relatively prime numbers
Recognize that 6 and 7 are relatively prime, i.e., they share no common factors except 1. Familiarize yourself with prime numbers up to 10 to make the calculations like this simpler, the numbers are 2,3,5,7.
Not realizing that numbers 6 and 7 are relatively prime will lead to over complicating the problem. The LCM, in the case of relatively prime numbers, is simply their product.
Therefore, the LCM of numbers 6 and 7 is 42 (7×6=42).
LCM of 6 and 7 Examples
Problem 1
What is the least perfect square divisible by 6 and 7?
Follow the below steps to find the least perfect square that is divisible by the numbers 6 and 7;
Step 1 — Prime factorize the numbers
6 = 2×3
7 = 7
Step 2 — Find the LCM
LCM(6,7) = 2×3×7 = 42
Step 3 — Adjust the numbers for a perfect square, to do so to make all the exponents even. Multiply the numbers
21×31×71, which will give;
42×42 = 22×32×72 = 1764
Explanation
The least perfect square divisible by both the numbers is 1764.
Problem 2
Elaborate on the relationship between HCF and LCM of 6 and 7.
The relationship between HCF and LCM can be verified using this formula; HCF(a,b)×LCM(a,b) = a×b
HCF of 6,7 = 1 (6,7 are relatively prime numbers)
LCM of 6,7 = 42
Now apply the formula,
HCF(a,b)×LCM(a,b) = a×b
HCF(6,7)×LCM(6,7) = 6×7
1×42 = 42
42 = 42
Explanation
The above explains the relationship between the HCF and the LCM of 6 and 7. The given formula works to verify the relationship between the HCF and LCM for any given pair of numbers.
Problem 3
Find the LCM of 6 and 7 using a Venn diagram.
List the factors of the numbers;
— 6 —> 2,3
— 7 —> 7
Explanation
The numbers have no common factors, therefore the numbers are listed in their own circles and are multiplied. The LCM (6,7) = 42.
Problem 4
Elevator F stops on the first floor every 6 minutes and elevator Y stops every 7 minutes. If they both stop on the first floor now, when will they both stop at the same time next?
The LCM of 6 and 7 is 42.
Explanation
The smallest common multiple between the numbers 6 and 7 is 42. So, we can say that in 42 minutes, elevators F and Y will stop at the same time on the first floor.
FAQs on LCM of 6 and 7
1.What do 6 and 7 have in common?
2.Is 42 a multiple of 6 and 7?
3.Is 69 a multiple of 6?
4.Is 42 the LCM of 6 and 7?
5.What is the LCM of 6,7 and 9?
Important glossaries for the LCM of 6 and 7
- Prime Factor: A natural number (other than 1) whose factors are only one and itself.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
- Relatively Prime Numbers: Numbers that have no common factors other than 1.
