Least Common Multiple of 84 and 90

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 90 the smallest integer that is 1260 that is divisible by both numbers.

Least Common Multiple (LCM) of 84 and 90 is 1260.

LCM(84,90) = 1260

LCM of 84 and 90

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

LCM of:
and

Least Common Multiple of 84 and 90

LCM of 84 and 90 is 1260

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 90. First we will calculate the prime factors of 84 and 90.

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 90


2 90
3 45
3 15
5 5
1

Prime factors of 90 are 2, 3,5. Prime factorization of 90 in exponential form is:

90 = 21×32×51

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 90.

LCM(84,90) = 22×32×51×71
LCM(84,90) = 1260

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 90

List of positive integer factors of 90 that divides 90 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Least Common Multiple of 84 and 90 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 90, than apply into the LCM equation.

GCF(84,90) = 6
LCM(84,90) = ( 84 × 90) / 6
LCM(84,90) = 7560 / 6
LCM(84,90) = 1260

Properties of LCM 84 and 90

(i) The LCM of 90 and 84 is associative

LCM of 84 and 90 = LCM of 90 and 84

Related Least Common Multiples of 84

Related Least Common Multiples of 90

Frequently Asked Questions on LCM of 84 and 90

1. What is the LCM of 84 and 90?

Answer: LCM of 84 and 90 is 1260.

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 90?

Answer: Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. There are 12 integers that are factors of 90. The greatest factor of 90 is 90.

4. How to Find the LCM of 84 and 90?

Answer:

Least Common Multiple of 84 and 90 = 1260

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 90

90 = 2 x 3 x 3 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 = 1260 = 2 x 2 x 3 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 84 and 90 is 1260.