Least Common Multiple of 821 and 825

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 821 and 825 the smallest integer that is 677325 that is divisible by both numbers.

Least Common Multiple (LCM) of 821 and 825 is 677325.

LCM(821,825) = 677325

LCM of 821 and 825

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

LCM of:
and

Least Common Multiple of 821 and 825

LCM of 821 and 825 is 677325

Least common multiple can be found by multiplying the highest exponent prime factors of 821 and 825. First we will calculate the prime factors of 821 and 825.

Prime Factorization of 821


821 821
1

Prime factors of 821 are 821. Prime factorization of 821 in exponential form is:

821 = 8211

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

Now multiplying the highest exponent prime factors to calculate the LCM of 821 and 825.

LCM(821,825) = 31×52×111×8211
LCM(821,825) = 677325

Factors of 821

List of positive integer factors of 821 that divides 821 without a remainder.

1, 821

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

Least Common Multiple of 821 and 825 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 821 and 825, than apply into the LCM equation.

GCF(821,825) = 1
LCM(821,825) = ( 821 × 825) / 1
LCM(821,825) = 677325 / 1
LCM(821,825) = 677325

Properties of LCM 821 and 825

(i) The LCM of 825 and 821 is associative

LCM of 821 and 825 = LCM of 825 and 821

Related Least Common Multiples of 821

Related Least Common Multiples of 825

Frequently Asked Questions on LCM of 821 and 825

1. What is the LCM of 821 and 825?

Answer: LCM of 821 and 825 is 677325.

2. What are the Factors of 821?

Answer: Factors of 821 are 1, 821. There are 2 integers that are factors of 821. The greatest factor of 821 is 821.

3. 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.

4. How to Find the LCM of 821 and 825?

Answer:

Least Common Multiple of 821 and 825 = 677325

Step 1: Find the prime factorization of 821

821 = 821

Step 2: Find the prime factorization of 825

825 = 3 x 5 x 5 x 11

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

LCM = 677325 = 3 x 5 x 5 x 11 x 821

Step 4: Therefore, the least common multiple of 821 and 825 is 677325.