Least Common Multiple of 1824 and 1830

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 1830 the smallest integer that is 556320 that is divisible by both numbers.

Least Common Multiple (LCM) of 1824 and 1830 is 556320.

LCM(1824,1830) = 556320

LCM of 1824 and 1830

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

LCM of:
and

Least Common Multiple of 1824 and 1830

LCM of 1824 and 1830 is 556320

Least common multiple can be found by multiplying the highest exponent prime factors of 1824 and 1830. First we will calculate the prime factors of 1824 and 1830.

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 1830


2 1830
3 915
5 305
61 61
1

Prime factors of 1830 are 2, 3, 5,61. Prime factorization of 1830 in exponential form is:

1830 = 21×31×51×611

Now multiplying the highest exponent prime factors to calculate the LCM of 1824 and 1830.

LCM(1824,1830) = 25×31×51×191×611
LCM(1824,1830) = 556320

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 1830

List of positive integer factors of 1830 that divides 1830 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 61, 122, 183, 305, 366, 610, 915, 1830

Least Common Multiple of 1824 and 1830 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 1830, than apply into the LCM equation.

GCF(1824,1830) = 6
LCM(1824,1830) = ( 1824 × 1830) / 6
LCM(1824,1830) = 3337920 / 6
LCM(1824,1830) = 556320

Properties of LCM 1824 and 1830

(i) The LCM of 1830 and 1824 is associative

LCM of 1824 and 1830 = LCM of 1830 and 1824

Related Least Common Multiples of 1824

Related Least Common Multiples of 1830

Frequently Asked Questions on LCM of 1824 and 1830

1. What is the LCM of 1824 and 1830?

Answer: LCM of 1824 and 1830 is 556320.

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 1830?

Answer: Factors of 1830 are 1, 2, 3, 5, 6, 10, 15, 30, 61, 122, 183, 305, 366, 610, 915, 1830. There are 16 integers that are factors of 1830. The greatest factor of 1830 is 1830.

4. How to Find the LCM of 1824 and 1830?

Answer:

Least Common Multiple of 1824 and 1830 = 556320

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 1830

1830 = 2 x 3 x 5 x 61

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

LCM = 556320 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 19 x 61

Step 4: Therefore, the least common multiple of 1824 and 1830 is 556320.