Least Common Multiple of 7824 and 7828

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7824 and 7828 the smallest integer that is 15311568 that is divisible by both numbers.

Least Common Multiple (LCM) of 7824 and 7828 is 15311568.

LCM(7824,7828) = 15311568

LCM of 7824 and 7828

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

LCM of:
and

Least Common Multiple of 7824 and 7828

LCM of 7824 and 7828 is 15311568

Least common multiple can be found by multiplying the highest exponent prime factors of 7824 and 7828. First we will calculate the prime factors of 7824 and 7828.

Prime Factorization of 7824


2 7824
2 3912
2 1956
2 978
3 489
163 163
1

Prime factors of 7824 are 2, 3,163. Prime factorization of 7824 in exponential form is:

7824 = 24×31×1631

Prime Factorization of 7828


2 7828
2 3914
19 1957
103 103
1

Prime factors of 7828 are 2, 19,103. Prime factorization of 7828 in exponential form is:

7828 = 22×191×1031

Now multiplying the highest exponent prime factors to calculate the LCM of 7824 and 7828.

LCM(7824,7828) = 24×31×191×1031×1631
LCM(7824,7828) = 15311568

Factors of 7824

List of positive integer factors of 7824 that divides 7824 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 163, 326, 489, 652, 978, 1304, 1956, 2608, 3912, 7824

Factors of 7828

List of positive integer factors of 7828 that divides 7828 without a remainder.

1, 2, 4, 19, 38, 76, 103, 206, 412, 1957, 3914, 7828

Least Common Multiple of 7824 and 7828 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7824 and 7828, than apply into the LCM equation.

GCF(7824,7828) = 4
LCM(7824,7828) = ( 7824 × 7828) / 4
LCM(7824,7828) = 61246272 / 4
LCM(7824,7828) = 15311568

Properties of LCM 7824 and 7828

(i) The LCM of 7828 and 7824 is associative

LCM of 7824 and 7828 = LCM of 7828 and 7824

Related Least Common Multiples of 7824

Related Least Common Multiples of 7828

Frequently Asked Questions on LCM of 7824 and 7828

1. What is the LCM of 7824 and 7828?

Answer: LCM of 7824 and 7828 is 15311568.

2. What are the Factors of 7824?

Answer: Factors of 7824 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 163, 326, 489, 652, 978, 1304, 1956, 2608, 3912, 7824. There are 20 integers that are factors of 7824. The greatest factor of 7824 is 7824.

3. What are the Factors of 7828?

Answer: Factors of 7828 are 1, 2, 4, 19, 38, 76, 103, 206, 412, 1957, 3914, 7828. There are 12 integers that are factors of 7828. The greatest factor of 7828 is 7828.

4. How to Find the LCM of 7824 and 7828?

Answer:

Least Common Multiple of 7824 and 7828 = 15311568

Step 1: Find the prime factorization of 7824

7824 = 2 x 2 x 2 x 2 x 3 x 163

Step 2: Find the prime factorization of 7828

7828 = 2 x 2 x 19 x 103

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

LCM = 15311568 = 2 x 2 x 2 x 2 x 3 x 19 x 103 x 163

Step 4: Therefore, the least common multiple of 7824 and 7828 is 15311568.