Least Common Multiple of 126 and 132

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 126 and 132 the smallest integer that is 2772 that is divisible by both numbers.

Least Common Multiple (LCM) of 126 and 132 is 2772.

LCM(126,132) = 2772

LCM of 126 and 132

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 126 and 132

LCM of 126 and 132 is 2772

Least common multiple can be found by multiplying the highest exponent prime factors of 126 and 132. First we will calculate the prime factors of 126 and 132.

Prime Factorization of 126


2 126
3 63
3 21
7 7
1

Prime factors of 126 are 2, 3,7. Prime factorization of 126 in exponential form is:

126 = 21×32×71

Prime Factorization of 132


2 132
2 66
3 33
11 11
1

Prime factors of 132 are 2, 3,11. Prime factorization of 132 in exponential form is:

132 = 22×31×111

Now multiplying the highest exponent prime factors to calculate the LCM of 126 and 132.

LCM(126,132) = 22×32×71×111
LCM(126,132) = 2772

Factors of 126

List of positive integer factors of 126 that divides 126 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

Factors of 132

List of positive integer factors of 132 that divides 132 without a remainder.

1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132

Least Common Multiple of 126 and 132 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 126 and 132, than apply into the LCM equation.

GCF(126,132) = 6
LCM(126,132) = ( 126 × 132) / 6
LCM(126,132) = 16632 / 6
LCM(126,132) = 2772

Properties of LCM 126 and 132

(i) The LCM of 132 and 126 is associative

LCM of 126 and 132 = LCM of 132 and 126

Related Least Common Multiples of 126

Related Least Common Multiples of 132

Frequently Asked Questions on LCM of 126 and 132

1. What is the LCM of 126 and 132?

Answer: LCM of 126 and 132 is 2772.

2. What are the Factors of 126?

Answer: Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. There are 12 integers that are factors of 126. The greatest factor of 126 is 126.

3. What are the Factors of 132?

Answer: Factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132. There are 12 integers that are factors of 132. The greatest factor of 132 is 132.

4. How to Find the LCM of 126 and 132?

Answer:

Least Common Multiple of 126 and 132 = 2772

Step 1: Find the prime factorization of 126

126 = 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 132

132 = 2 x 2 x 3 x 11

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2772 = 2 x 2 x 3 x 3 x 7 x 11

Step 4: Therefore, the least common multiple of 126 and 132 is 2772.