Least Common Multiple of 78 and 81

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 81 the smallest integer that is 2106 that is divisible by both numbers.

Least Common Multiple (LCM) of 78 and 81 is 2106.

LCM(78,81) = 2106

LCM of 78 and 81

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

LCM of:
and

Least Common Multiple of 78 and 81

LCM of 78 and 81 is 2106

Least common multiple can be found by multiplying the highest exponent prime factors of 78 and 81. First we will calculate the prime factors of 78 and 81.

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 81


3 81
3 27
3 9
3 3
1

Prime factors of 81 are 3. Prime factorization of 81 in exponential form is:

81 = 34

Now multiplying the highest exponent prime factors to calculate the LCM of 78 and 81.

LCM(78,81) = 21×34×131
LCM(78,81) = 2106

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 81

List of positive integer factors of 81 that divides 81 without a remainder.

1, 3, 9, 27, 81

Least Common Multiple of 78 and 81 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 81, than apply into the LCM equation.

GCF(78,81) = 3
LCM(78,81) = ( 78 × 81) / 3
LCM(78,81) = 6318 / 3
LCM(78,81) = 2106

Properties of LCM 78 and 81

(i) The LCM of 81 and 78 is associative

LCM of 78 and 81 = LCM of 81 and 78

Related Least Common Multiples of 78

Related Least Common Multiples of 81

Frequently Asked Questions on LCM of 78 and 81

1. What is the LCM of 78 and 81?

Answer: LCM of 78 and 81 is 2106.

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 81?

Answer: Factors of 81 are 1, 3, 9, 27, 81. There are 5 integers that are factors of 81. The greatest factor of 81 is 81.

4. How to Find the LCM of 78 and 81?

Answer:

Least Common Multiple of 78 and 81 = 2106

Step 1: Find the prime factorization of 78

78 = 2 x 3 x 13

Step 2: Find the prime factorization of 81

81 = 3 x 3 x 3 x 3

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

LCM = 2106 = 2 x 3 x 3 x 3 x 3 x 13

Step 4: Therefore, the least common multiple of 78 and 81 is 2106.