Least Common Multiple of 1896 and 1900

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1896 and 1900 the smallest integer that is 900600 that is divisible by both numbers.

Least Common Multiple (LCM) of 1896 and 1900 is 900600.

LCM(1896,1900) = 900600

LCM of 1896 and 1900

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

LCM of:
and

Least Common Multiple of 1896 and 1900

LCM of 1896 and 1900 is 900600

Least common multiple can be found by multiplying the highest exponent prime factors of 1896 and 1900. First we will calculate the prime factors of 1896 and 1900.

Prime Factorization of 1896


2 1896
2 948
2 474
3 237
79 79
1

Prime factors of 1896 are 2, 3,79. Prime factorization of 1896 in exponential form is:

1896 = 23×31×791

Prime Factorization of 1900


2 1900
2 950
5 475
5 95
19 19
1

Prime factors of 1900 are 2, 5,19. Prime factorization of 1900 in exponential form is:

1900 = 22×52×191

Now multiplying the highest exponent prime factors to calculate the LCM of 1896 and 1900.

LCM(1896,1900) = 23×31×52×191×791
LCM(1896,1900) = 900600

Factors of 1896

List of positive integer factors of 1896 that divides 1896 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 79, 158, 237, 316, 474, 632, 948, 1896

Factors of 1900

List of positive integer factors of 1900 that divides 1900 without a remainder.

1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 190, 380, 475, 950, 1900

Least Common Multiple of 1896 and 1900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1896 and 1900, than apply into the LCM equation.

GCF(1896,1900) = 4
LCM(1896,1900) = ( 1896 × 1900) / 4
LCM(1896,1900) = 3602400 / 4
LCM(1896,1900) = 900600

Properties of LCM 1896 and 1900

(i) The LCM of 1900 and 1896 is associative

LCM of 1896 and 1900 = LCM of 1900 and 1896

Related Least Common Multiples of 1896

Related Least Common Multiples of 1900

Frequently Asked Questions on LCM of 1896 and 1900

1. What is the LCM of 1896 and 1900?

Answer: LCM of 1896 and 1900 is 900600.

2. What are the Factors of 1896?

Answer: Factors of 1896 are 1, 2, 3, 4, 6, 8, 12, 24, 79, 158, 237, 316, 474, 632, 948, 1896. There are 16 integers that are factors of 1896. The greatest factor of 1896 is 1896.

3. What are the Factors of 1900?

Answer: Factors of 1900 are 1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 190, 380, 475, 950, 1900. There are 18 integers that are factors of 1900. The greatest factor of 1900 is 1900.

4. How to Find the LCM of 1896 and 1900?

Answer:

Least Common Multiple of 1896 and 1900 = 900600

Step 1: Find the prime factorization of 1896

1896 = 2 x 2 x 2 x 3 x 79

Step 2: Find the prime factorization of 1900

1900 = 2 x 2 x 5 x 5 x 19

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

LCM = 900600 = 2 x 2 x 2 x 3 x 5 x 5 x 19 x 79

Step 4: Therefore, the least common multiple of 1896 and 1900 is 900600.