Least Common Multiple of 748 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 748 and 756 the smallest integer that is 141372 that is divisible by both numbers.

Least Common Multiple (LCM) of 748 and 756 is 141372.

LCM(748,756) = 141372

LCM of 748 and 756

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

LCM of:
and

Least Common Multiple of 748 and 756

LCM of 748 and 756 is 141372

Least common multiple can be found by multiplying the highest exponent prime factors of 748 and 756. First we will calculate the prime factors of 748 and 756.

Prime Factorization of 748


2 748
2 374
11 187
17 17
1

Prime factors of 748 are 2, 11,17. Prime factorization of 748 in exponential form is:

748 = 22×111×171

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 748 and 756.

LCM(748,756) = 22×33×71×111×171
LCM(748,756) = 141372

Factors of 748

List of positive integer factors of 748 that divides 748 without a remainder.

1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748

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 748 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 748 and 756, than apply into the LCM equation.

GCF(748,756) = 4
LCM(748,756) = ( 748 × 756) / 4
LCM(748,756) = 565488 / 4
LCM(748,756) = 141372

Properties of LCM 748 and 756

(i) The LCM of 756 and 748 is associative

LCM of 748 and 756 = LCM of 756 and 748

Related Least Common Multiples of 748

Related Least Common Multiples of 756

Frequently Asked Questions on LCM of 748 and 756

1. What is the LCM of 748 and 756?

Answer: LCM of 748 and 756 is 141372.

2. What are the Factors of 748?

Answer: Factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748. There are 12 integers that are factors of 748. The greatest factor of 748 is 748.

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 748 and 756?

Answer:

Least Common Multiple of 748 and 756 = 141372

Step 1: Find the prime factorization of 748

748 = 2 x 2 x 11 x 17

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 = 141372 = 2 x 2 x 3 x 3 x 3 x 7 x 11 x 17

Step 4: Therefore, the least common multiple of 748 and 756 is 141372.