Least Common Multiple of 1575 and 1580

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1575 and 1580 the smallest integer that is 497700 that is divisible by both numbers.

Least Common Multiple (LCM) of 1575 and 1580 is 497700.

LCM(1575,1580) = 497700

LCM of 1575 and 1580

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

LCM of:
and

Least Common Multiple of 1575 and 1580

LCM of 1575 and 1580 is 497700

Least common multiple can be found by multiplying the highest exponent prime factors of 1575 and 1580. First we will calculate the prime factors of 1575 and 1580.

Prime Factorization of 1575


3 1575
3 525
5 175
5 35
7 7
1

Prime factors of 1575 are 3, 5,7. Prime factorization of 1575 in exponential form is:

1575 = 32×52×71

Prime Factorization of 1580


2 1580
2 790
5 395
79 79
1

Prime factors of 1580 are 2, 5,79. Prime factorization of 1580 in exponential form is:

1580 = 22×51×791

Now multiplying the highest exponent prime factors to calculate the LCM of 1575 and 1580.

LCM(1575,1580) = 22×32×52×71×791
LCM(1575,1580) = 497700

Factors of 1575

List of positive integer factors of 1575 that divides 1575 without a remainder.

1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575

Factors of 1580

List of positive integer factors of 1580 that divides 1580 without a remainder.

1, 2, 4, 5, 10, 20, 79, 158, 316, 395, 790, 1580

Least Common Multiple of 1575 and 1580 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1575 and 1580, than apply into the LCM equation.

GCF(1575,1580) = 5
LCM(1575,1580) = ( 1575 × 1580) / 5
LCM(1575,1580) = 2488500 / 5
LCM(1575,1580) = 497700

Properties of LCM 1575 and 1580

(i) The LCM of 1580 and 1575 is associative

LCM of 1575 and 1580 = LCM of 1580 and 1575

Related Least Common Multiples of 1575

Related Least Common Multiples of 1580

Frequently Asked Questions on LCM of 1575 and 1580

1. What is the LCM of 1575 and 1580?

Answer: LCM of 1575 and 1580 is 497700.

2. What are the Factors of 1575?

Answer: Factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575. There are 18 integers that are factors of 1575. The greatest factor of 1575 is 1575.

3. What are the Factors of 1580?

Answer: Factors of 1580 are 1, 2, 4, 5, 10, 20, 79, 158, 316, 395, 790, 1580. There are 12 integers that are factors of 1580. The greatest factor of 1580 is 1580.

4. How to Find the LCM of 1575 and 1580?

Answer:

Least Common Multiple of 1575 and 1580 = 497700

Step 1: Find the prime factorization of 1575

1575 = 3 x 3 x 5 x 5 x 7

Step 2: Find the prime factorization of 1580

1580 = 2 x 2 x 5 x 79

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

LCM = 497700 = 2 x 2 x 3 x 3 x 5 x 5 x 7 x 79

Step 4: Therefore, the least common multiple of 1575 and 1580 is 497700.