Least Common Multiple of 68 and 76

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 68 and 76 the smallest integer that is 1292 that is divisible by both numbers.

Least Common Multiple (LCM) of 68 and 76 is 1292.

LCM(68,76) = 1292

LCM of 68 and 76

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

LCM of:
and

Least Common Multiple of 68 and 76

LCM of 68 and 76 is 1292

Least common multiple can be found by multiplying the highest exponent prime factors of 68 and 76. First we will calculate the prime factors of 68 and 76.

Prime Factorization of 68


2 68
2 34
17 17
1

Prime factors of 68 are 2,17. Prime factorization of 68 in exponential form is:

68 = 22×171

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

Now multiplying the highest exponent prime factors to calculate the LCM of 68 and 76.

LCM(68,76) = 22×171×191
LCM(68,76) = 1292

Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1, 2, 4, 17, 34, 68

Factors of 76

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

1, 2, 4, 19, 38, 76

Least Common Multiple of 68 and 76 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 68 and 76, than apply into the LCM equation.

GCF(68,76) = 4
LCM(68,76) = ( 68 × 76) / 4
LCM(68,76) = 5168 / 4
LCM(68,76) = 1292

Properties of LCM 68 and 76

(i) The LCM of 76 and 68 is associative

LCM of 68 and 76 = LCM of 76 and 68

Related Least Common Multiples of 68

Related Least Common Multiples of 76

Frequently Asked Questions on LCM of 68 and 76

1. What is the LCM of 68 and 76?

Answer: LCM of 68 and 76 is 1292.

2. What are the Factors of 68?

Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.

3. 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.

4. How to Find the LCM of 68 and 76?

Answer:

Least Common Multiple of 68 and 76 = 1292

Step 1: Find the prime factorization of 68

68 = 2 x 2 x 17

Step 2: Find the prime factorization of 76

76 = 2 x 2 x 19

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

LCM = 1292 = 2 x 2 x 17 x 19

Step 4: Therefore, the least common multiple of 68 and 76 is 1292.