Least Common Multiple of 748 and 750

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 750 the smallest integer that is 280500 that is divisible by both numbers.

Least Common Multiple (LCM) of 748 and 750 is 280500.

LCM(748,750) = 280500

LCM of 748 and 750

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

LCM of:
and

Least Common Multiple of 748 and 750

LCM of 748 and 750 is 280500

Least common multiple can be found by multiplying the highest exponent prime factors of 748 and 750. First we will calculate the prime factors of 748 and 750.

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 750


2 750
3 375
5 125
5 25
5 5
1

Prime factors of 750 are 2, 3,5. Prime factorization of 750 in exponential form is:

750 = 21×31×53

Now multiplying the highest exponent prime factors to calculate the LCM of 748 and 750.

LCM(748,750) = 22×31×53×111×171
LCM(748,750) = 280500

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 750

List of positive integer factors of 750 that divides 750 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750

Least Common Multiple of 748 and 750 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 750, than apply into the LCM equation.

GCF(748,750) = 2
LCM(748,750) = ( 748 × 750) / 2
LCM(748,750) = 561000 / 2
LCM(748,750) = 280500

Properties of LCM 748 and 750

(i) The LCM of 750 and 748 is associative

LCM of 748 and 750 = LCM of 750 and 748

Related Least Common Multiples of 748

Related Least Common Multiples of 750

Frequently Asked Questions on LCM of 748 and 750

1. What is the LCM of 748 and 750?

Answer: LCM of 748 and 750 is 280500.

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 750?

Answer: Factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750. There are 16 integers that are factors of 750. The greatest factor of 750 is 750.

4. How to Find the LCM of 748 and 750?

Answer:

Least Common Multiple of 748 and 750 = 280500

Step 1: Find the prime factorization of 748

748 = 2 x 2 x 11 x 17

Step 2: Find the prime factorization of 750

750 = 2 x 3 x 5 x 5 x 5

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

LCM = 280500 = 2 x 2 x 3 x 5 x 5 x 5 x 11 x 17

Step 4: Therefore, the least common multiple of 748 and 750 is 280500.