Least Common Multiple of 1585 and 1590

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1585 and 1590 the smallest integer that is 504030 that is divisible by both numbers.

Least Common Multiple (LCM) of 1585 and 1590 is 504030.

LCM(1585,1590) = 504030

LCM of 1585 and 1590

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

LCM of:
and

Least Common Multiple of 1585 and 1590

LCM of 1585 and 1590 is 504030

Least common multiple can be found by multiplying the highest exponent prime factors of 1585 and 1590. First we will calculate the prime factors of 1585 and 1590.

Prime Factorization of 1585


5 1585
317 317
1

Prime factors of 1585 are 5,317. Prime factorization of 1585 in exponential form is:

1585 = 51×3171

Prime Factorization of 1590


2 1590
3 795
5 265
53 53
1

Prime factors of 1590 are 2, 3, 5,53. Prime factorization of 1590 in exponential form is:

1590 = 21×31×51×531

Now multiplying the highest exponent prime factors to calculate the LCM of 1585 and 1590.

LCM(1585,1590) = 21×31×51×531×3171
LCM(1585,1590) = 504030

Factors of 1585

List of positive integer factors of 1585 that divides 1585 without a remainder.

1, 5, 317, 1585

Factors of 1590

List of positive integer factors of 1590 that divides 1590 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795, 1590

Least Common Multiple of 1585 and 1590 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1585 and 1590, than apply into the LCM equation.

GCF(1585,1590) = 5
LCM(1585,1590) = ( 1585 × 1590) / 5
LCM(1585,1590) = 2520150 / 5
LCM(1585,1590) = 504030

Properties of LCM 1585 and 1590

(i) The LCM of 1590 and 1585 is associative

LCM of 1585 and 1590 = LCM of 1590 and 1585

Related Least Common Multiples of 1585

Related Least Common Multiples of 1590

Frequently Asked Questions on LCM of 1585 and 1590

1. What is the LCM of 1585 and 1590?

Answer: LCM of 1585 and 1590 is 504030.

2. What are the Factors of 1585?

Answer: Factors of 1585 are 1, 5, 317, 1585. There are 4 integers that are factors of 1585. The greatest factor of 1585 is 1585.

3. What are the Factors of 1590?

Answer: Factors of 1590 are 1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795, 1590. There are 16 integers that are factors of 1590. The greatest factor of 1590 is 1590.

4. How to Find the LCM of 1585 and 1590?

Answer:

Least Common Multiple of 1585 and 1590 = 504030

Step 1: Find the prime factorization of 1585

1585 = 5 x 317

Step 2: Find the prime factorization of 1590

1590 = 2 x 3 x 5 x 53

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

LCM = 504030 = 2 x 3 x 5 x 53 x 317

Step 4: Therefore, the least common multiple of 1585 and 1590 is 504030.