Least Common Multiple of 75 and 80

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 80 the smallest integer that is 1200 that is divisible by both numbers.

Least Common Multiple (LCM) of 75 and 80 is 1200.

LCM(75,80) = 1200

LCM of 75 and 80

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

LCM of:
and

Least Common Multiple of 75 and 80

LCM of 75 and 80 is 1200

Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 80. First we will calculate the prime factors of 75 and 80.

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 80


2 80
2 40
2 20
2 10
5 5
1

Prime factors of 80 are 2,5. Prime factorization of 80 in exponential form is:

80 = 24×51

Now multiplying the highest exponent prime factors to calculate the LCM of 75 and 80.

LCM(75,80) = 24×31×52
LCM(75,80) = 1200

Factors of 75

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

1, 3, 5, 15, 25, 75

Factors of 80

List of positive integer factors of 80 that divides 80 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80

Least Common Multiple of 75 and 80 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 80, than apply into the LCM equation.

GCF(75,80) = 5
LCM(75,80) = ( 75 × 80) / 5
LCM(75,80) = 6000 / 5
LCM(75,80) = 1200

Properties of LCM 75 and 80

(i) The LCM of 80 and 75 is associative

LCM of 75 and 80 = LCM of 80 and 75

Related Least Common Multiples of 75

Related Least Common Multiples of 80

Frequently Asked Questions on LCM of 75 and 80

1. What is the LCM of 75 and 80?

Answer: LCM of 75 and 80 is 1200.

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 80?

Answer: Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. There are 10 integers that are factors of 80. The greatest factor of 80 is 80.

4. How to Find the LCM of 75 and 80?

Answer:

Least Common Multiple of 75 and 80 = 1200

Step 1: Find the prime factorization of 75

75 = 3 x 5 x 5

Step 2: Find the prime factorization of 80

80 = 2 x 2 x 2 x 2 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 = 1200 = 2 x 2 x 2 x 2 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 75 and 80 is 1200.