Least Common Multiple of 1824 and 1828

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1824 and 1828 the smallest integer that is 833568 that is divisible by both numbers.

Least Common Multiple (LCM) of 1824 and 1828 is 833568.

LCM(1824,1828) = 833568

LCM of 1824 and 1828

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

LCM of:
and

Least Common Multiple of 1824 and 1828

LCM of 1824 and 1828 is 833568

Least common multiple can be found by multiplying the highest exponent prime factors of 1824 and 1828. First we will calculate the prime factors of 1824 and 1828.

Prime Factorization of 1824


2 1824
2 912
2 456
2 228
2 114
3 57
19 19
1

Prime factors of 1824 are 2, 3,19. Prime factorization of 1824 in exponential form is:

1824 = 25×31×191

Prime Factorization of 1828


2 1828
2 914
457 457
1

Prime factors of 1828 are 2,457. Prime factorization of 1828 in exponential form is:

1828 = 22×4571

Now multiplying the highest exponent prime factors to calculate the LCM of 1824 and 1828.

LCM(1824,1828) = 25×31×191×4571
LCM(1824,1828) = 833568

Factors of 1824

List of positive integer factors of 1824 that divides 1824 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 456, 608, 912, 1824

Factors of 1828

List of positive integer factors of 1828 that divides 1828 without a remainder.

1, 2, 4, 457, 914, 1828

Least Common Multiple of 1824 and 1828 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1824 and 1828, than apply into the LCM equation.

GCF(1824,1828) = 4
LCM(1824,1828) = ( 1824 × 1828) / 4
LCM(1824,1828) = 3334272 / 4
LCM(1824,1828) = 833568

Properties of LCM 1824 and 1828

(i) The LCM of 1828 and 1824 is associative

LCM of 1824 and 1828 = LCM of 1828 and 1824

Related Least Common Multiples of 1824

Related Least Common Multiples of 1828

Frequently Asked Questions on LCM of 1824 and 1828

1. What is the LCM of 1824 and 1828?

Answer: LCM of 1824 and 1828 is 833568.

2. What are the Factors of 1824?

Answer: Factors of 1824 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 456, 608, 912, 1824. There are 24 integers that are factors of 1824. The greatest factor of 1824 is 1824.

3. What are the Factors of 1828?

Answer: Factors of 1828 are 1, 2, 4, 457, 914, 1828. There are 6 integers that are factors of 1828. The greatest factor of 1828 is 1828.

4. How to Find the LCM of 1824 and 1828?

Answer:

Least Common Multiple of 1824 and 1828 = 833568

Step 1: Find the prime factorization of 1824

1824 = 2 x 2 x 2 x 2 x 2 x 3 x 19

Step 2: Find the prime factorization of 1828

1828 = 2 x 2 x 457

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

LCM = 833568 = 2 x 2 x 2 x 2 x 2 x 3 x 19 x 457

Step 4: Therefore, the least common multiple of 1824 and 1828 is 833568.