Least Common Multiple of 1584 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 1584 and 1590 the smallest integer that is 419760 that is divisible by both numbers.

Least Common Multiple (LCM) of 1584 and 1590 is 419760.

LCM(1584,1590) = 419760

LCM of 1584 and 1590

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

LCM of:
and

Least Common Multiple of 1584 and 1590

LCM of 1584 and 1590 is 419760

Least common multiple can be found by multiplying the highest exponent prime factors of 1584 and 1590. First we will calculate the prime factors of 1584 and 1590.

Prime Factorization of 1584


2 1584
2 792
2 396
2 198
3 99
3 33
11 11
1

Prime factors of 1584 are 2, 3,11. Prime factorization of 1584 in exponential form is:

1584 = 24×32×111

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 1584 and 1590.

LCM(1584,1590) = 24×32×51×111×531
LCM(1584,1590) = 419760

Factors of 1584

List of positive integer factors of 1584 that divides 1584 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 132, 144, 176, 198, 264, 396, 528, 792, 1584

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 1584 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 1584 and 1590, than apply into the LCM equation.

GCF(1584,1590) = 6
LCM(1584,1590) = ( 1584 × 1590) / 6
LCM(1584,1590) = 2518560 / 6
LCM(1584,1590) = 419760

Properties of LCM 1584 and 1590

(i) The LCM of 1590 and 1584 is associative

LCM of 1584 and 1590 = LCM of 1590 and 1584

Related Least Common Multiples of 1584

Related Least Common Multiples of 1590

Frequently Asked Questions on LCM of 1584 and 1590

1. What is the LCM of 1584 and 1590?

Answer: LCM of 1584 and 1590 is 419760.

2. What are the Factors of 1584?

Answer: Factors of 1584 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 132, 144, 176, 198, 264, 396, 528, 792, 1584. There are 30 integers that are factors of 1584. The greatest factor of 1584 is 1584.

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 1584 and 1590?

Answer:

Least Common Multiple of 1584 and 1590 = 419760

Step 1: Find the prime factorization of 1584

1584 = 2 x 2 x 2 x 2 x 3 x 3 x 11

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 = 419760 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11 x 53

Step 4: Therefore, the least common multiple of 1584 and 1590 is 419760.