Least Common Multiple of 64 and 75

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 64 and 75 the smallest integer that is 4800 that is divisible by both numbers.

Least Common Multiple (LCM) of 64 and 75 is 4800.

LCM(64,75) = 4800

LCM of 64 and 75

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

LCM of:
and

Least Common Multiple of 64 and 75

LCM of 64 and 75 is 4800

Least common multiple can be found by multiplying the highest exponent prime factors of 64 and 75. First we will calculate the prime factors of 64 and 75.

Prime Factorization of 64


2 64
2 32
2 16
2 8
2 4
2 2
1

Prime factors of 64 are 2. Prime factorization of 64 in exponential form is:

64 = 26

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

Now multiplying the highest exponent prime factors to calculate the LCM of 64 and 75.

LCM(64,75) = 26×31×52
LCM(64,75) = 4800

Factors of 64

List of positive integer factors of 64 that divides 64 without a remainder.

1, 2, 4, 8, 16, 32, 64

Factors of 75

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

1, 3, 5, 15, 25, 75

Least Common Multiple of 64 and 75 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 64 and 75, than apply into the LCM equation.

GCF(64,75) = 1
LCM(64,75) = ( 64 × 75) / 1
LCM(64,75) = 4800 / 1
LCM(64,75) = 4800

Properties of LCM 64 and 75

(i) The LCM of 75 and 64 is associative

LCM of 64 and 75 = LCM of 75 and 64

Related Least Common Multiples of 64

Related Least Common Multiples of 75

Frequently Asked Questions on LCM of 64 and 75

1. What is the LCM of 64 and 75?

Answer: LCM of 64 and 75 is 4800.

2. What are the Factors of 64?

Answer: Factors of 64 are 1, 2, 4, 8, 16, 32, 64. There are 7 integers that are factors of 64. The greatest factor of 64 is 64.

3. 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.

4. How to Find the LCM of 64 and 75?

Answer:

Least Common Multiple of 64 and 75 = 4800

Step 1: Find the prime factorization of 64

64 = 2 x 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 75

75 = 3 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 = 4800 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 64 and 75 is 4800.