Least Common Multiple of 892 and 900

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 892 and 900 the smallest integer that is 200700 that is divisible by both numbers.

Least Common Multiple (LCM) of 892 and 900 is 200700.

LCM(892,900) = 200700

LCM of 892 and 900

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

LCM of:
and

Least Common Multiple of 892 and 900

LCM of 892 and 900 is 200700

Least common multiple can be found by multiplying the highest exponent prime factors of 892 and 900. First we will calculate the prime factors of 892 and 900.

Prime Factorization of 892


2 892
2 446
223 223
1

Prime factors of 892 are 2,223. Prime factorization of 892 in exponential form is:

892 = 22×2231

Prime Factorization of 900


2 900
2 450
3 225
3 75
5 25
5 5
1

Prime factors of 900 are 2, 3,5. Prime factorization of 900 in exponential form is:

900 = 22×32×52

Now multiplying the highest exponent prime factors to calculate the LCM of 892 and 900.

LCM(892,900) = 22×32×52×2231
LCM(892,900) = 200700

Factors of 892

List of positive integer factors of 892 that divides 892 without a remainder.

1, 2, 4, 223, 446, 892

Factors of 900

List of positive integer factors of 900 that divides 900 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900

Least Common Multiple of 892 and 900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 892 and 900, than apply into the LCM equation.

GCF(892,900) = 4
LCM(892,900) = ( 892 × 900) / 4
LCM(892,900) = 802800 / 4
LCM(892,900) = 200700

Properties of LCM 892 and 900

(i) The LCM of 900 and 892 is associative

LCM of 892 and 900 = LCM of 900 and 892

Related Least Common Multiples of 892

Related Least Common Multiples of 900

Frequently Asked Questions on LCM of 892 and 900

1. What is the LCM of 892 and 900?

Answer: LCM of 892 and 900 is 200700.

2. What are the Factors of 892?

Answer: Factors of 892 are 1, 2, 4, 223, 446, 892. There are 6 integers that are factors of 892. The greatest factor of 892 is 892.

3. What are the Factors of 900?

Answer: Factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900. There are 27 integers that are factors of 900. The greatest factor of 900 is 900.

4. How to Find the LCM of 892 and 900?

Answer:

Least Common Multiple of 892 and 900 = 200700

Step 1: Find the prime factorization of 892

892 = 2 x 2 x 223

Step 2: Find the prime factorization of 900

900 = 2 x 2 x 3 x 3 x 5 x 5

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

LCM = 200700 = 2 x 2 x 3 x 3 x 5 x 5 x 223

Step 4: Therefore, the least common multiple of 892 and 900 is 200700.