Least Common Multiple of 64 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 64 and 78 the smallest integer that is 2496 that is divisible by both numbers.

Least Common Multiple (LCM) of 64 and 78 is 2496.

LCM(64,78) = 2496

LCM of 64 and 78

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

LCM of:
and

Least Common Multiple of 64 and 78

LCM of 64 and 78 is 2496

Least common multiple can be found by multiplying the highest exponent prime factors of 64 and 78. First we will calculate the prime factors of 64 and 78.

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 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 64 and 78.

LCM(64,78) = 26×31×131
LCM(64,78) = 2496

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 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 64 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 64 and 78, than apply into the LCM equation.

GCF(64,78) = 2
LCM(64,78) = ( 64 × 78) / 2
LCM(64,78) = 4992 / 2
LCM(64,78) = 2496

Properties of LCM 64 and 78

(i) The LCM of 78 and 64 is associative

LCM of 64 and 78 = LCM of 78 and 64

Related Least Common Multiples of 64

Related Least Common Multiples of 78

Frequently Asked Questions on LCM of 64 and 78

1. What is the LCM of 64 and 78?

Answer: LCM of 64 and 78 is 2496.

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 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 64 and 78?

Answer:

Least Common Multiple of 64 and 78 = 2496

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 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 = 2496 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13

Step 4: Therefore, the least common multiple of 64 and 78 is 2496.