Least Common Multiple of 85 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 85 and 90 the smallest integer that is 1530 that is divisible by both numbers.

Least Common Multiple (LCM) of 85 and 90 is 1530.

LCM(85,90) = 1530

LCM of 85 and 90

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

LCM of:
and

Least Common Multiple of 85 and 90

LCM of 85 and 90 is 1530

Least common multiple can be found by multiplying the highest exponent prime factors of 85 and 90. First we will calculate the prime factors of 85 and 90.

Prime Factorization of 85


5 85
17 17
1

Prime factors of 85 are 5,17. Prime factorization of 85 in exponential form is:

85 = 51×171

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 85 and 90.

LCM(85,90) = 21×32×51×171
LCM(85,90) = 1530

Factors of 85

List of positive integer factors of 85 that divides 85 without a remainder.

1, 5, 17, 85

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 85 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 85 and 90, than apply into the LCM equation.

GCF(85,90) = 5
LCM(85,90) = ( 85 × 90) / 5
LCM(85,90) = 7650 / 5
LCM(85,90) = 1530

Properties of LCM 85 and 90

(i) The LCM of 90 and 85 is associative

LCM of 85 and 90 = LCM of 90 and 85

Related Least Common Multiples of 85

Related Least Common Multiples of 90

Frequently Asked Questions on LCM of 85 and 90

1. What is the LCM of 85 and 90?

Answer: LCM of 85 and 90 is 1530.

2. What are the Factors of 85?

Answer: Factors of 85 are 1, 5, 17, 85. There are 4 integers that are factors of 85. The greatest factor of 85 is 85.

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 85 and 90?

Answer:

Least Common Multiple of 85 and 90 = 1530

Step 1: Find the prime factorization of 85

85 = 5 x 17

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 = 1530 = 2 x 3 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 85 and 90 is 1530.