Least Common Multiple of 1584 and 1592

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 1592 the smallest integer that is 315216 that is divisible by both numbers.

Least Common Multiple (LCM) of 1584 and 1592 is 315216.

LCM(1584,1592) = 315216

LCM of 1584 and 1592

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

LCM of:
and

Least Common Multiple of 1584 and 1592

LCM of 1584 and 1592 is 315216

Least common multiple can be found by multiplying the highest exponent prime factors of 1584 and 1592. First we will calculate the prime factors of 1584 and 1592.

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 1592


2 1592
2 796
2 398
199 199
1

Prime factors of 1592 are 2,199. Prime factorization of 1592 in exponential form is:

1592 = 23×1991

Now multiplying the highest exponent prime factors to calculate the LCM of 1584 and 1592.

LCM(1584,1592) = 24×32×111×1991
LCM(1584,1592) = 315216

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 1592

List of positive integer factors of 1592 that divides 1592 without a remainder.

1, 2, 4, 8, 199, 398, 796, 1592

Least Common Multiple of 1584 and 1592 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 1592, than apply into the LCM equation.

GCF(1584,1592) = 8
LCM(1584,1592) = ( 1584 × 1592) / 8
LCM(1584,1592) = 2521728 / 8
LCM(1584,1592) = 315216

Properties of LCM 1584 and 1592

(i) The LCM of 1592 and 1584 is associative

LCM of 1584 and 1592 = LCM of 1592 and 1584

Related Least Common Multiples of 1584

Related Least Common Multiples of 1592

Frequently Asked Questions on LCM of 1584 and 1592

1. What is the LCM of 1584 and 1592?

Answer: LCM of 1584 and 1592 is 315216.

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 1592?

Answer: Factors of 1592 are 1, 2, 4, 8, 199, 398, 796, 1592. There are 8 integers that are factors of 1592. The greatest factor of 1592 is 1592.

4. How to Find the LCM of 1584 and 1592?

Answer:

Least Common Multiple of 1584 and 1592 = 315216

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 1592

1592 = 2 x 2 x 2 x 199

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

LCM = 315216 = 2 x 2 x 2 x 2 x 3 x 3 x 11 x 199

Step 4: Therefore, the least common multiple of 1584 and 1592 is 315216.