Least Common Multiple of 78 and 84

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 84 the smallest integer that is 1092 that is divisible by both numbers.

Least Common Multiple (LCM) of 78 and 84 is 1092.

LCM(78,84) = 1092

LCM of 78 and 84

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

LCM of:
and

Least Common Multiple of 78 and 84

LCM of 78 and 84 is 1092

Least common multiple can be found by multiplying the highest exponent prime factors of 78 and 84. First we will calculate the prime factors of 78 and 84.

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 84


2 84
2 42
3 21
7 7
1

Prime factors of 84 are 2, 3,7. Prime factorization of 84 in exponential form is:

84 = 22×31×71

Now multiplying the highest exponent prime factors to calculate the LCM of 78 and 84.

LCM(78,84) = 22×31×71×131
LCM(78,84) = 1092

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 84

List of positive integer factors of 84 that divides 84 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Least Common Multiple of 78 and 84 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 84, than apply into the LCM equation.

GCF(78,84) = 6
LCM(78,84) = ( 78 × 84) / 6
LCM(78,84) = 6552 / 6
LCM(78,84) = 1092

Properties of LCM 78 and 84

(i) The LCM of 84 and 78 is associative

LCM of 78 and 84 = LCM of 84 and 78

Related Least Common Multiples of 78

Related Least Common Multiples of 84

Frequently Asked Questions on LCM of 78 and 84

1. What is the LCM of 78 and 84?

Answer: LCM of 78 and 84 is 1092.

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 84?

Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.

4. How to Find the LCM of 78 and 84?

Answer:

Least Common Multiple of 78 and 84 = 1092

Step 1: Find the prime factorization of 78

78 = 2 x 3 x 13

Step 2: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

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

LCM = 1092 = 2 x 2 x 3 x 7 x 13

Step 4: Therefore, the least common multiple of 78 and 84 is 1092.