Least Common Multiple of 825 and 828

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 825 and 828 the smallest integer that is 227700 that is divisible by both numbers.

Least Common Multiple (LCM) of 825 and 828 is 227700.

LCM(825,828) = 227700

LCM of 825 and 828

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

LCM of:
and

Least Common Multiple of 825 and 828

LCM of 825 and 828 is 227700

Least common multiple can be found by multiplying the highest exponent prime factors of 825 and 828. First we will calculate the prime factors of 825 and 828.

Prime Factorization of 825


3 825
5 275
5 55
11 11
1

Prime factors of 825 are 3, 5,11. Prime factorization of 825 in exponential form is:

825 = 31×52×111

Prime Factorization of 828


2 828
2 414
3 207
3 69
23 23
1

Prime factors of 828 are 2, 3,23. Prime factorization of 828 in exponential form is:

828 = 22×32×231

Now multiplying the highest exponent prime factors to calculate the LCM of 825 and 828.

LCM(825,828) = 22×32×52×111×231
LCM(825,828) = 227700

Factors of 825

List of positive integer factors of 825 that divides 825 without a remainder.

1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825

Factors of 828

List of positive integer factors of 828 that divides 828 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828

Least Common Multiple of 825 and 828 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 825 and 828, than apply into the LCM equation.

GCF(825,828) = 3
LCM(825,828) = ( 825 × 828) / 3
LCM(825,828) = 683100 / 3
LCM(825,828) = 227700

Properties of LCM 825 and 828

(i) The LCM of 828 and 825 is associative

LCM of 825 and 828 = LCM of 828 and 825

Related Least Common Multiples of 825

Related Least Common Multiples of 828

Frequently Asked Questions on LCM of 825 and 828

1. What is the LCM of 825 and 828?

Answer: LCM of 825 and 828 is 227700.

2. What are the Factors of 825?

Answer: Factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825. There are 12 integers that are factors of 825. The greatest factor of 825 is 825.

3. What are the Factors of 828?

Answer: Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828. There are 18 integers that are factors of 828. The greatest factor of 828 is 828.

4. How to Find the LCM of 825 and 828?

Answer:

Least Common Multiple of 825 and 828 = 227700

Step 1: Find the prime factorization of 825

825 = 3 x 5 x 5 x 11

Step 2: Find the prime factorization of 828

828 = 2 x 2 x 3 x 3 x 23

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

LCM = 227700 = 2 x 2 x 3 x 3 x 5 x 5 x 11 x 23

Step 4: Therefore, the least common multiple of 825 and 828 is 227700.