Least Common Multiple of 126 and 129

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 129 the smallest integer that is 5418 that is divisible by both numbers.

Least Common Multiple (LCM) of 126 and 129 is 5418.

LCM(126,129) = 5418

LCM of 126 and 129

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

LCM of:
and

Least Common Multiple of 126 and 129

LCM of 126 and 129 is 5418

Least common multiple can be found by multiplying the highest exponent prime factors of 126 and 129. First we will calculate the prime factors of 126 and 129.

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 129


3 129
43 43
1

Prime factors of 129 are 3,43. Prime factorization of 129 in exponential form is:

129 = 31×431

Now multiplying the highest exponent prime factors to calculate the LCM of 126 and 129.

LCM(126,129) = 21×32×71×431
LCM(126,129) = 5418

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 129

List of positive integer factors of 129 that divides 129 without a remainder.

1, 3, 43, 129

Least Common Multiple of 126 and 129 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 129, than apply into the LCM equation.

GCF(126,129) = 3
LCM(126,129) = ( 126 × 129) / 3
LCM(126,129) = 16254 / 3
LCM(126,129) = 5418

Properties of LCM 126 and 129

(i) The LCM of 129 and 126 is associative

LCM of 126 and 129 = LCM of 129 and 126

Related Least Common Multiples of 126

Related Least Common Multiples of 129

Frequently Asked Questions on LCM of 126 and 129

1. What is the LCM of 126 and 129?

Answer: LCM of 126 and 129 is 5418.

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 129?

Answer: Factors of 129 are 1, 3, 43, 129. There are 4 integers that are factors of 129. The greatest factor of 129 is 129.

4. How to Find the LCM of 126 and 129?

Answer:

Least Common Multiple of 126 and 129 = 5418

Step 1: Find the prime factorization of 126

126 = 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 129

129 = 3 x 43

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

LCM = 5418 = 2 x 3 x 3 x 7 x 43

Step 4: Therefore, the least common multiple of 126 and 129 is 5418.