Least Common Multiple of 76 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 76 and 78 the smallest integer that is 2964 that is divisible by both numbers.

Least Common Multiple (LCM) of 76 and 78 is 2964.

LCM(76,78) = 2964

LCM of 76 and 78

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

LCM of:
and

Least Common Multiple of 76 and 78

LCM of 76 and 78 is 2964

Least common multiple can be found by multiplying the highest exponent prime factors of 76 and 78. First we will calculate the prime factors of 76 and 78.

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

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 76 and 78.

LCM(76,78) = 22×31×131×191
LCM(76,78) = 2964

Factors of 76

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

1, 2, 4, 19, 38, 76

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 76 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 76 and 78, than apply into the LCM equation.

GCF(76,78) = 2
LCM(76,78) = ( 76 × 78) / 2
LCM(76,78) = 5928 / 2
LCM(76,78) = 2964

Properties of LCM 76 and 78

(i) The LCM of 78 and 76 is associative

LCM of 76 and 78 = LCM of 78 and 76

Related Least Common Multiples of 76

Related Least Common Multiples of 78

Frequently Asked Questions on LCM of 76 and 78

1. What is the LCM of 76 and 78?

Answer: LCM of 76 and 78 is 2964.

2. 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.

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 76 and 78?

Answer:

Least Common Multiple of 76 and 78 = 2964

Step 1: Find the prime factorization of 76

76 = 2 x 2 x 19

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 = 2964 = 2 x 2 x 3 x 13 x 19

Step 4: Therefore, the least common multiple of 76 and 78 is 2964.