Least Common Multiple of 75 and 76

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 75 and 76 the smallest integer that is 5700 that is divisible by both numbers.

Least Common Multiple (LCM) of 75 and 76 is 5700.

LCM(75,76) = 5700

LCM of 75 and 76

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

LCM of:
and

Least Common Multiple of 75 and 76

LCM of 75 and 76 is 5700

Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 76. First we will calculate the prime factors of 75 and 76.

Prime Factorization of 75


3 75
5 25
5 5
1

Prime factors of 75 are 3,5. Prime factorization of 75 in exponential form is:

75 = 31×52

Prime Factorization of 76


2 76
2 38
19 19
1

Prime factors of 76 are 2,19. Prime factorization of 76 in exponential form is:

76 = 22×191

Now multiplying the highest exponent prime factors to calculate the LCM of 75 and 76.

LCM(75,76) = 22×31×52×191
LCM(75,76) = 5700

Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1, 3, 5, 15, 25, 75

Factors of 76

List of positive integer factors of 76 that divides 76 without a remainder.

1, 2, 4, 19, 38, 76

Least Common Multiple of 75 and 76 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75 and 76, than apply into the LCM equation.

GCF(75,76) = 1
LCM(75,76) = ( 75 × 76) / 1
LCM(75,76) = 5700 / 1
LCM(75,76) = 5700

Properties of LCM 75 and 76

(i) The LCM of 76 and 75 is associative

LCM of 75 and 76 = LCM of 76 and 75

Related Least Common Multiples of 75

Related Least Common Multiples of 76

Frequently Asked Questions on LCM of 75 and 76

1. What is the LCM of 75 and 76?

Answer: LCM of 75 and 76 is 5700.

2. What are the Factors of 75?

Answer: Factors of 75 are 1, 3, 5, 15, 25, 75. There are 6 integers that are factors of 75. The greatest factor of 75 is 75.

3. What are the Factors of 76?

Answer: Factors of 76 are 1, 2, 4, 19, 38, 76. There are 6 integers that are factors of 76. The greatest factor of 76 is 76.

4. How to Find the LCM of 75 and 76?

Answer:

Least Common Multiple of 75 and 76 = 5700

Step 1: Find the prime factorization of 75

75 = 3 x 5 x 5

Step 2: Find the prime factorization of 76

76 = 2 x 2 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 = 5700 = 2 x 2 x 3 x 5 x 5 x 19

Step 4: Therefore, the least common multiple of 75 and 76 is 5700.