Least Common Multiple of 1820 and 1824

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1820 and 1824 the smallest integer that is 829920 that is divisible by both numbers.

Least Common Multiple (LCM) of 1820 and 1824 is 829920.

LCM(1820,1824) = 829920

LCM of 1820 and 1824

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

LCM of:
and

Least Common Multiple of 1820 and 1824

LCM of 1820 and 1824 is 829920

Least common multiple can be found by multiplying the highest exponent prime factors of 1820 and 1824. First we will calculate the prime factors of 1820 and 1824.

Prime Factorization of 1820


2 1820
2 910
5 455
7 91
13 13
1

Prime factors of 1820 are 2, 5, 7,13. Prime factorization of 1820 in exponential form is:

1820 = 22×51×71×131

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1820 and 1824.

LCM(1820,1824) = 25×31×51×71×131×191
LCM(1820,1824) = 829920

Factors of 1820

List of positive integer factors of 1820 that divides 1820 without a remainder.

1, 2, 4, 5, 7, 10, 13, 14, 20, 26, 28, 35, 52, 65, 70, 91, 130, 140, 182, 260, 364, 455, 910, 1820

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

Least Common Multiple of 1820 and 1824 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1820 and 1824, than apply into the LCM equation.

GCF(1820,1824) = 4
LCM(1820,1824) = ( 1820 × 1824) / 4
LCM(1820,1824) = 3319680 / 4
LCM(1820,1824) = 829920

Properties of LCM 1820 and 1824

(i) The LCM of 1824 and 1820 is associative

LCM of 1820 and 1824 = LCM of 1824 and 1820

Related Least Common Multiples of 1820

Related Least Common Multiples of 1824

Frequently Asked Questions on LCM of 1820 and 1824

1. What is the LCM of 1820 and 1824?

Answer: LCM of 1820 and 1824 is 829920.

2. What are the Factors of 1820?

Answer: Factors of 1820 are 1, 2, 4, 5, 7, 10, 13, 14, 20, 26, 28, 35, 52, 65, 70, 91, 130, 140, 182, 260, 364, 455, 910, 1820. There are 24 integers that are factors of 1820. The greatest factor of 1820 is 1820.

3. 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.

4. How to Find the LCM of 1820 and 1824?

Answer:

Least Common Multiple of 1820 and 1824 = 829920

Step 1: Find the prime factorization of 1820

1820 = 2 x 2 x 5 x 7 x 13

Step 2: Find the prime factorization of 1824

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

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

LCM = 829920 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 13 x 19

Step 4: Therefore, the least common multiple of 1820 and 1824 is 829920.