Least Common Multiple of 1578 and 1584

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1578 and 1584 the smallest integer that is 416592 that is divisible by both numbers.

Least Common Multiple (LCM) of 1578 and 1584 is 416592.

LCM(1578,1584) = 416592

LCM of 1578 and 1584

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

LCM of:
and

Least Common Multiple of 1578 and 1584

LCM of 1578 and 1584 is 416592

Least common multiple can be found by multiplying the highest exponent prime factors of 1578 and 1584. First we will calculate the prime factors of 1578 and 1584.

Prime Factorization of 1578


2 1578
3 789
263 263
1

Prime factors of 1578 are 2, 3,263. Prime factorization of 1578 in exponential form is:

1578 = 21×31×2631

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1578 and 1584.

LCM(1578,1584) = 24×32×111×2631
LCM(1578,1584) = 416592

Factors of 1578

List of positive integer factors of 1578 that divides 1578 without a remainder.

1, 2, 3, 6, 263, 526, 789, 1578

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

Least Common Multiple of 1578 and 1584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1578 and 1584, than apply into the LCM equation.

GCF(1578,1584) = 6
LCM(1578,1584) = ( 1578 × 1584) / 6
LCM(1578,1584) = 2499552 / 6
LCM(1578,1584) = 416592

Properties of LCM 1578 and 1584

(i) The LCM of 1584 and 1578 is associative

LCM of 1578 and 1584 = LCM of 1584 and 1578

Related Least Common Multiples of 1578

Related Least Common Multiples of 1584

Frequently Asked Questions on LCM of 1578 and 1584

1. What is the LCM of 1578 and 1584?

Answer: LCM of 1578 and 1584 is 416592.

2. What are the Factors of 1578?

Answer: Factors of 1578 are 1, 2, 3, 6, 263, 526, 789, 1578. There are 8 integers that are factors of 1578. The greatest factor of 1578 is 1578.

3. 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.

4. How to Find the LCM of 1578 and 1584?

Answer:

Least Common Multiple of 1578 and 1584 = 416592

Step 1: Find the prime factorization of 1578

1578 = 2 x 3 x 263

Step 2: Find the prime factorization of 1584

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

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

LCM = 416592 = 2 x 2 x 2 x 2 x 3 x 3 x 11 x 263

Step 4: Therefore, the least common multiple of 1578 and 1584 is 416592.