Least Common Multiple of 1596 and 1600

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1596 and 1600 the smallest integer that is 638400 that is divisible by both numbers.

Least Common Multiple (LCM) of 1596 and 1600 is 638400.

LCM(1596,1600) = 638400

LCM of 1596 and 1600

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

LCM of:
and

Least Common Multiple of 1596 and 1600

LCM of 1596 and 1600 is 638400

Least common multiple can be found by multiplying the highest exponent prime factors of 1596 and 1600. First we will calculate the prime factors of 1596 and 1600.

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

Prime Factorization of 1600


2 1600
2 800
2 400
2 200
2 100
2 50
5 25
5 5
1

Prime factors of 1600 are 2,5. Prime factorization of 1600 in exponential form is:

1600 = 26×52

Now multiplying the highest exponent prime factors to calculate the LCM of 1596 and 1600.

LCM(1596,1600) = 26×31×52×71×191
LCM(1596,1600) = 638400

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

Factors of 1600

List of positive integer factors of 1600 that divides 1600 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600

Least Common Multiple of 1596 and 1600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1596 and 1600, than apply into the LCM equation.

GCF(1596,1600) = 4
LCM(1596,1600) = ( 1596 × 1600) / 4
LCM(1596,1600) = 2553600 / 4
LCM(1596,1600) = 638400

Properties of LCM 1596 and 1600

(i) The LCM of 1600 and 1596 is associative

LCM of 1596 and 1600 = LCM of 1600 and 1596

Related Least Common Multiples of 1596

Related Least Common Multiples of 1600

Frequently Asked Questions on LCM of 1596 and 1600

1. What is the LCM of 1596 and 1600?

Answer: LCM of 1596 and 1600 is 638400.

2. 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.

3. What are the Factors of 1600?

Answer: Factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600. There are 21 integers that are factors of 1600. The greatest factor of 1600 is 1600.

4. How to Find the LCM of 1596 and 1600?

Answer:

Least Common Multiple of 1596 and 1600 = 638400

Step 1: Find the prime factorization of 1596

1596 = 2 x 2 x 3 x 7 x 19

Step 2: Find the prime factorization of 1600

1600 = 2 x 2 x 2 x 2 x 2 x 2 x 5 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 = 638400 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 19

Step 4: Therefore, the least common multiple of 1596 and 1600 is 638400.