Least Common Multiple of 126 and 133

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 133 the smallest integer that is 2394 that is divisible by both numbers.

Least Common Multiple (LCM) of 126 and 133 is 2394.

LCM(126,133) = 2394

LCM of 126 and 133

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

LCM of:
and

Least Common Multiple of 126 and 133

LCM of 126 and 133 is 2394

Least common multiple can be found by multiplying the highest exponent prime factors of 126 and 133. First we will calculate the prime factors of 126 and 133.

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 133


7 133
19 19
1

Prime factors of 133 are 7,19. Prime factorization of 133 in exponential form is:

133 = 71×191

Now multiplying the highest exponent prime factors to calculate the LCM of 126 and 133.

LCM(126,133) = 21×32×71×191
LCM(126,133) = 2394

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 133

List of positive integer factors of 133 that divides 133 without a remainder.

1, 7, 19, 133

Least Common Multiple of 126 and 133 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 133, than apply into the LCM equation.

GCF(126,133) = 7
LCM(126,133) = ( 126 × 133) / 7
LCM(126,133) = 16758 / 7
LCM(126,133) = 2394

Properties of LCM 126 and 133

(i) The LCM of 133 and 126 is associative

LCM of 126 and 133 = LCM of 133 and 126

Related Least Common Multiples of 126

Related Least Common Multiples of 133

Frequently Asked Questions on LCM of 126 and 133

1. What is the LCM of 126 and 133?

Answer: LCM of 126 and 133 is 2394.

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 133?

Answer: Factors of 133 are 1, 7, 19, 133. There are 4 integers that are factors of 133. The greatest factor of 133 is 133.

4. How to Find the LCM of 126 and 133?

Answer:

Least Common Multiple of 126 and 133 = 2394

Step 1: Find the prime factorization of 126

126 = 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 133

133 = 7 x 19

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

LCM = 2394 = 2 x 3 x 3 x 7 x 19

Step 4: Therefore, the least common multiple of 126 and 133 is 2394.