Least Common Multiple of 749 and 756

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 749 and 756 the smallest integer that is 80892 that is divisible by both numbers.

Least Common Multiple (LCM) of 749 and 756 is 80892.

LCM(749,756) = 80892

LCM of 749 and 756

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

LCM of:
and

Least Common Multiple of 749 and 756

LCM of 749 and 756 is 80892

Least common multiple can be found by multiplying the highest exponent prime factors of 749 and 756. First we will calculate the prime factors of 749 and 756.

Prime Factorization of 749


7 749
107 107
1

Prime factors of 749 are 7,107. Prime factorization of 749 in exponential form is:

749 = 71×1071

Prime Factorization of 756


2 756
2 378
3 189
3 63
3 21
7 7
1

Prime factors of 756 are 2, 3,7. Prime factorization of 756 in exponential form is:

756 = 22×33×71

Now multiplying the highest exponent prime factors to calculate the LCM of 749 and 756.

LCM(749,756) = 22×33×71×1071
LCM(749,756) = 80892

Factors of 749

List of positive integer factors of 749 that divides 749 without a remainder.

1, 7, 107, 749

Factors of 756

List of positive integer factors of 756 that divides 756 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756

Least Common Multiple of 749 and 756 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 749 and 756, than apply into the LCM equation.

GCF(749,756) = 7
LCM(749,756) = ( 749 × 756) / 7
LCM(749,756) = 566244 / 7
LCM(749,756) = 80892

Properties of LCM 749 and 756

(i) The LCM of 756 and 749 is associative

LCM of 749 and 756 = LCM of 756 and 749

Related Least Common Multiples of 749

Related Least Common Multiples of 756

Frequently Asked Questions on LCM of 749 and 756

1. What is the LCM of 749 and 756?

Answer: LCM of 749 and 756 is 80892.

2. What are the Factors of 749?

Answer: Factors of 749 are 1, 7, 107, 749. There are 4 integers that are factors of 749. The greatest factor of 749 is 749.

3. What are the Factors of 756?

Answer: Factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756. There are 24 integers that are factors of 756. The greatest factor of 756 is 756.

4. How to Find the LCM of 749 and 756?

Answer:

Least Common Multiple of 749 and 756 = 80892

Step 1: Find the prime factorization of 749

749 = 7 x 107

Step 2: Find the prime factorization of 756

756 = 2 x 2 x 3 x 3 x 3 x 7

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

LCM = 80892 = 2 x 2 x 3 x 3 x 3 x 7 x 107

Step 4: Therefore, the least common multiple of 749 and 756 is 80892.