Least Common Multiple of 78 and 80

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 80 the smallest integer that is 3120 that is divisible by both numbers.

Least Common Multiple (LCM) of 78 and 80 is 3120.

LCM(78,80) = 3120

LCM of 78 and 80

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

LCM of:
and

Least Common Multiple of 78 and 80

LCM of 78 and 80 is 3120

Least common multiple can be found by multiplying the highest exponent prime factors of 78 and 80. First we will calculate the prime factors of 78 and 80.

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 80


2 80
2 40
2 20
2 10
5 5
1

Prime factors of 80 are 2,5. Prime factorization of 80 in exponential form is:

80 = 24×51

Now multiplying the highest exponent prime factors to calculate the LCM of 78 and 80.

LCM(78,80) = 24×31×51×131
LCM(78,80) = 3120

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 80

List of positive integer factors of 80 that divides 80 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80

Least Common Multiple of 78 and 80 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 80, than apply into the LCM equation.

GCF(78,80) = 2
LCM(78,80) = ( 78 × 80) / 2
LCM(78,80) = 6240 / 2
LCM(78,80) = 3120

Properties of LCM 78 and 80

(i) The LCM of 80 and 78 is associative

LCM of 78 and 80 = LCM of 80 and 78

Related Least Common Multiples of 78

Related Least Common Multiples of 80

Frequently Asked Questions on LCM of 78 and 80

1. What is the LCM of 78 and 80?

Answer: LCM of 78 and 80 is 3120.

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 80?

Answer: Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. There are 10 integers that are factors of 80. The greatest factor of 80 is 80.

4. How to Find the LCM of 78 and 80?

Answer:

Least Common Multiple of 78 and 80 = 3120

Step 1: Find the prime factorization of 78

78 = 2 x 3 x 13

Step 2: Find the prime factorization of 80

80 = 2 x 2 x 2 x 2 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 = 3120 = 2 x 2 x 2 x 2 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 78 and 80 is 3120.