Least Common Multiple of 896 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 896 and 900 the smallest integer that is 201600 that is divisible by both numbers.

Least Common Multiple (LCM) of 896 and 900 is 201600.

LCM(896,900) = 201600

LCM of 896 and 900

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

LCM of:
and

Least Common Multiple of 896 and 900

LCM of 896 and 900 is 201600

Least common multiple can be found by multiplying the highest exponent prime factors of 896 and 900. First we will calculate the prime factors of 896 and 900.

Prime Factorization of 896


2 896
2 448
2 224
2 112
2 56
2 28
2 14
7 7
1

Prime factors of 896 are 2,7. Prime factorization of 896 in exponential form is:

896 = 27×71

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 896 and 900.

LCM(896,900) = 27×32×52×71
LCM(896,900) = 201600

Factors of 896

List of positive integer factors of 896 that divides 896 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896

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 896 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 896 and 900, than apply into the LCM equation.

GCF(896,900) = 4
LCM(896,900) = ( 896 × 900) / 4
LCM(896,900) = 806400 / 4
LCM(896,900) = 201600

Properties of LCM 896 and 900

(i) The LCM of 900 and 896 is associative

LCM of 896 and 900 = LCM of 900 and 896

Related Least Common Multiples of 896

Related Least Common Multiples of 900

Frequently Asked Questions on LCM of 896 and 900

1. What is the LCM of 896 and 900?

Answer: LCM of 896 and 900 is 201600.

2. What are the Factors of 896?

Answer: Factors of 896 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896. There are 16 integers that are factors of 896. The greatest factor of 896 is 896.

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 896 and 900?

Answer:

Least Common Multiple of 896 and 900 = 201600

Step 1: Find the prime factorization of 896

896 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7

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 = 201600 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7

Step 4: Therefore, the least common multiple of 896 and 900 is 201600.