Least Common Multiple of 75 and 78

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 78 the smallest integer that is 1950 that is divisible by both numbers.

Least Common Multiple (LCM) of 75 and 78 is 1950.

LCM(75,78) = 1950

LCM of 75 and 78

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

LCM of:
and

Least Common Multiple of 75 and 78

LCM of 75 and 78 is 1950

Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 78. First we will calculate the prime factors of 75 and 78.

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 78


2 78
3 39
13 13
1

Prime factors of 78 are 2, 3,13. Prime factorization of 78 in exponential form is:

78 = 21×31×131

Now multiplying the highest exponent prime factors to calculate the LCM of 75 and 78.

LCM(75,78) = 21×31×52×131
LCM(75,78) = 1950

Factors of 75

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

1, 3, 5, 15, 25, 75

Factors of 78

List of positive integer factors of 78 that divides 78 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78

Least Common Multiple of 75 and 78 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 78, than apply into the LCM equation.

GCF(75,78) = 3
LCM(75,78) = ( 75 × 78) / 3
LCM(75,78) = 5850 / 3
LCM(75,78) = 1950

Properties of LCM 75 and 78

(i) The LCM of 78 and 75 is associative

LCM of 75 and 78 = LCM of 78 and 75

Related Least Common Multiples of 75

Related Least Common Multiples of 78

Frequently Asked Questions on LCM of 75 and 78

1. What is the LCM of 75 and 78?

Answer: LCM of 75 and 78 is 1950.

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 78?

Answer: Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78. There are 8 integers that are factors of 78. The greatest factor of 78 is 78.

4. How to Find the LCM of 75 and 78?

Answer:

Least Common Multiple of 75 and 78 = 1950

Step 1: Find the prime factorization of 75

75 = 3 x 5 x 5

Step 2: Find the prime factorization of 78

78 = 2 x 3 x 13

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

LCM = 1950 = 2 x 3 x 5 x 5 x 13

Step 4: Therefore, the least common multiple of 75 and 78 is 1950.