Least Common Multiple of 78 and 83

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 78 and 83 the smallest integer that is 6474 that is divisible by both numbers.

Least Common Multiple (LCM) of 78 and 83 is 6474.

LCM(78,83) = 6474

LCM of 78 and 83

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

LCM of:
and

Least Common Multiple of 78 and 83

LCM of 78 and 83 is 6474

Least common multiple can be found by multiplying the highest exponent prime factors of 78 and 83. First we will calculate the prime factors of 78 and 83.

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

Prime Factorization of 83


83 83
1

Prime factors of 83 are 83. Prime factorization of 83 in exponential form is:

83 = 831

Now multiplying the highest exponent prime factors to calculate the LCM of 78 and 83.

LCM(78,83) = 21×31×131×831
LCM(78,83) = 6474

Factors of 78

List of positive integer factors of 78 that divides 78 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78

Factors of 83

List of positive integer factors of 83 that divides 83 without a remainder.

1, 83

Least Common Multiple of 78 and 83 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78 and 83, than apply into the LCM equation.

GCF(78,83) = 1
LCM(78,83) = ( 78 × 83) / 1
LCM(78,83) = 6474 / 1
LCM(78,83) = 6474

Properties of LCM 78 and 83

(i) The LCM of 83 and 78 is associative

LCM of 78 and 83 = LCM of 83 and 78

Related Least Common Multiples of 78

Related Least Common Multiples of 83

Frequently Asked Questions on LCM of 78 and 83

1. What is the LCM of 78 and 83?

Answer: LCM of 78 and 83 is 6474.

2. 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.

3. What are the Factors of 83?

Answer: Factors of 83 are 1, 83. There are 2 integers that are factors of 83. The greatest factor of 83 is 83.

4. How to Find the LCM of 78 and 83?

Answer:

Least Common Multiple of 78 and 83 = 6474

Step 1: Find the prime factorization of 78

78 = 2 x 3 x 13

Step 2: Find the prime factorization of 83

83 = 83

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

LCM = 6474 = 2 x 3 x 13 x 83

Step 4: Therefore, the least common multiple of 78 and 83 is 6474.