Least Common Multiple of 84 and 86

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 84 and 86 the smallest integer that is 3612 that is divisible by both numbers.

Least Common Multiple (LCM) of 84 and 86 is 3612.

LCM(84,86) = 3612

LCM of 84 and 86

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

LCM of:
and

Least Common Multiple of 84 and 86

LCM of 84 and 86 is 3612

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 86. First we will calculate the prime factors of 84 and 86.

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

Prime Factorization of 86


2 86
43 43
1

Prime factors of 86 are 2,43. Prime factorization of 86 in exponential form is:

86 = 21×431

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 86.

LCM(84,86) = 22×31×71×431
LCM(84,86) = 3612

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

Factors of 86

List of positive integer factors of 86 that divides 86 without a remainder.

1, 2, 43, 86

Least Common Multiple of 84 and 86 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84 and 86, than apply into the LCM equation.

GCF(84,86) = 2
LCM(84,86) = ( 84 × 86) / 2
LCM(84,86) = 7224 / 2
LCM(84,86) = 3612

Properties of LCM 84 and 86

(i) The LCM of 86 and 84 is associative

LCM of 84 and 86 = LCM of 86 and 84

Related Least Common Multiples of 84

Related Least Common Multiples of 86

Frequently Asked Questions on LCM of 84 and 86

1. What is the LCM of 84 and 86?

Answer: LCM of 84 and 86 is 3612.

2. 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.

3. What are the Factors of 86?

Answer: Factors of 86 are 1, 2, 43, 86. There are 4 integers that are factors of 86. The greatest factor of 86 is 86.

4. How to Find the LCM of 84 and 86?

Answer:

Least Common Multiple of 84 and 86 = 3612

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 86

86 = 2 x 43

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

LCM = 3612 = 2 x 2 x 3 x 7 x 43

Step 4: Therefore, the least common multiple of 84 and 86 is 3612.