Least Common Multiple of 1590 and 1596

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1590 and 1596 the smallest integer that is 422940 that is divisible by both numbers.

Least Common Multiple (LCM) of 1590 and 1596 is 422940.

LCM(1590,1596) = 422940

LCM of 1590 and 1596

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

LCM of:
and

Least Common Multiple of 1590 and 1596

LCM of 1590 and 1596 is 422940

Least common multiple can be found by multiplying the highest exponent prime factors of 1590 and 1596. First we will calculate the prime factors of 1590 and 1596.

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

Prime Factorization of 1596


2 1596
2 798
3 399
7 133
19 19
1

Prime factors of 1596 are 2, 3, 7,19. Prime factorization of 1596 in exponential form is:

1596 = 22×31×71×191

Now multiplying the highest exponent prime factors to calculate the LCM of 1590 and 1596.

LCM(1590,1596) = 22×31×51×71×191×531
LCM(1590,1596) = 422940

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

Factors of 1596

List of positive integer factors of 1596 that divides 1596 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 19, 21, 28, 38, 42, 57, 76, 84, 114, 133, 228, 266, 399, 532, 798, 1596

Least Common Multiple of 1590 and 1596 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1590 and 1596, than apply into the LCM equation.

GCF(1590,1596) = 6
LCM(1590,1596) = ( 1590 × 1596) / 6
LCM(1590,1596) = 2537640 / 6
LCM(1590,1596) = 422940

Properties of LCM 1590 and 1596

(i) The LCM of 1596 and 1590 is associative

LCM of 1590 and 1596 = LCM of 1596 and 1590

Related Least Common Multiples of 1590

Related Least Common Multiples of 1596

Frequently Asked Questions on LCM of 1590 and 1596

1. What is the LCM of 1590 and 1596?

Answer: LCM of 1590 and 1596 is 422940.

2. 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.

3. What are the Factors of 1596?

Answer: Factors of 1596 are 1, 2, 3, 4, 6, 7, 12, 14, 19, 21, 28, 38, 42, 57, 76, 84, 114, 133, 228, 266, 399, 532, 798, 1596. There are 24 integers that are factors of 1596. The greatest factor of 1596 is 1596.

4. How to Find the LCM of 1590 and 1596?

Answer:

Least Common Multiple of 1590 and 1596 = 422940

Step 1: Find the prime factorization of 1590

1590 = 2 x 3 x 5 x 53

Step 2: Find the prime factorization of 1596

1596 = 2 x 2 x 3 x 7 x 19

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

LCM = 422940 = 2 x 2 x 3 x 5 x 7 x 19 x 53

Step 4: Therefore, the least common multiple of 1590 and 1596 is 422940.