Least Common Multiple of 6 and 7
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6 and 7 the smallest integer that is 42 that is divisible by both numbers.
Least Common Multiple (LCM) of 6 and 7 is 42.
LCM(6,7) = 42
LCM of 6 and 7
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
LCM of 6 and 7 is 42
Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 7. First we will calculate the prime factors of 6 and 7.
Prime Factorization of 6
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:
6 = 21×31
Prime Factorization of 7
| 7 | 7 |
| 1 |
Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:
7 = 71
Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 7.
LCM(6,7) = 21×31×71
LCM(6,7) = 42
Factors of 6
List of positive integer factors of 6 that divides 6 without a remainder.
1, 2, 3, 6
Factors of 7
List of positive integer factors of 7 that divides 7 without a remainder.
1, 7
Least Common Multiple of 6 and 7 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 7, than apply into the LCM equation.
GCF(6,7) = 1
LCM(6,7) = ( 6 × 7) / 1
LCM(6,7) = 42 / 1
LCM(6,7) = 42
Properties of LCM 6 and 7
(i) The LCM of 7 and 6 is associative
LCM of 6 and 7 = LCM of 7 and 6
Related Least Common Multiples of 6
Related Least Common Multiples of 7
Frequently Asked Questions on LCM of 6 and 7
1. What is the LCM of 6 and 7?
Answer: LCM of 6 and 7 is 42.
2. What are the Factors of 6?
Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.
3. What are the Factors of 7?
Answer: Factors of 7 are 1, 7. There are 2 integers that are factors of 7. The greatest factor of 7 is 7.
4. How to Find the LCM of 6 and 7?
Answer:
Least Common Multiple of 6 and 7 = 42
Step 1: Find the prime factorization of 6
6 = 2 x 3
Step 2: Find the prime factorization of 7
7 = 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 42 = 2 x 3 x 7
Step 4: Therefore, the least common multiple of 6 and 7 is 42.