Least Common Multiple of 1575 and 1582

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 1582 the smallest integer that is 355950 that is divisible by both numbers.

Least Common Multiple (LCM) of 1575 and 1582 is 355950.

LCM(1575,1582) = 355950

LCM of 1575 and 1582

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

LCM of:
and

Least Common Multiple of 1575 and 1582

LCM of 1575 and 1582 is 355950

Least common multiple can be found by multiplying the highest exponent prime factors of 1575 and 1582. First we will calculate the prime factors of 1575 and 1582.

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 1582


2 1582
7 791
113 113
1

Prime factors of 1582 are 2, 7,113. Prime factorization of 1582 in exponential form is:

1582 = 21×71×1131

Now multiplying the highest exponent prime factors to calculate the LCM of 1575 and 1582.

LCM(1575,1582) = 21×32×52×71×1131
LCM(1575,1582) = 355950

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 1582

List of positive integer factors of 1582 that divides 1582 without a remainder.

1, 2, 7, 14, 113, 226, 791, 1582

Least Common Multiple of 1575 and 1582 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 1582, than apply into the LCM equation.

GCF(1575,1582) = 7
LCM(1575,1582) = ( 1575 × 1582) / 7
LCM(1575,1582) = 2491650 / 7
LCM(1575,1582) = 355950

Properties of LCM 1575 and 1582

(i) The LCM of 1582 and 1575 is associative

LCM of 1575 and 1582 = LCM of 1582 and 1575

Related Least Common Multiples of 1575

Related Least Common Multiples of 1582

Frequently Asked Questions on LCM of 1575 and 1582

1. What is the LCM of 1575 and 1582?

Answer: LCM of 1575 and 1582 is 355950.

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 1582?

Answer: Factors of 1582 are 1, 2, 7, 14, 113, 226, 791, 1582. There are 8 integers that are factors of 1582. The greatest factor of 1582 is 1582.

4. How to Find the LCM of 1575 and 1582?

Answer:

Least Common Multiple of 1575 and 1582 = 355950

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 1582

1582 = 2 x 7 x 113

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

LCM = 355950 = 2 x 3 x 3 x 5 x 5 x 7 x 113

Step 4: Therefore, the least common multiple of 1575 and 1582 is 355950.