Least Common Multiple of 87 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 87 and 90 the smallest integer that is 2610 that is divisible by both numbers.

Least Common Multiple (LCM) of 87 and 90 is 2610.

LCM(87,90) = 2610

LCM of 87 and 90

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

LCM of:
and

Least Common Multiple of 87 and 90

LCM of 87 and 90 is 2610

Least common multiple can be found by multiplying the highest exponent prime factors of 87 and 90. First we will calculate the prime factors of 87 and 90.

Prime Factorization of 87


3 87
29 29
1

Prime factors of 87 are 3,29. Prime factorization of 87 in exponential form is:

87 = 31×291

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 87 and 90.

LCM(87,90) = 21×32×51×291
LCM(87,90) = 2610

Factors of 87

List of positive integer factors of 87 that divides 87 without a remainder.

1, 3, 29, 87

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 87 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 87 and 90, than apply into the LCM equation.

GCF(87,90) = 3
LCM(87,90) = ( 87 × 90) / 3
LCM(87,90) = 7830 / 3
LCM(87,90) = 2610

Properties of LCM 87 and 90

(i) The LCM of 90 and 87 is associative

LCM of 87 and 90 = LCM of 90 and 87

Related Least Common Multiples of 87

Related Least Common Multiples of 90

Frequently Asked Questions on LCM of 87 and 90

1. What is the LCM of 87 and 90?

Answer: LCM of 87 and 90 is 2610.

2. What are the Factors of 87?

Answer: Factors of 87 are 1, 3, 29, 87. There are 4 integers that are factors of 87. The greatest factor of 87 is 87.

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 87 and 90?

Answer:

Least Common Multiple of 87 and 90 = 2610

Step 1: Find the prime factorization of 87

87 = 3 x 29

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 = 2610 = 2 x 3 x 3 x 5 x 29

Step 4: Therefore, the least common multiple of 87 and 90 is 2610.