Least Common Multiple of 1900 and 1904

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1900 and 1904 the smallest integer that is 904400 that is divisible by both numbers.

Least Common Multiple (LCM) of 1900 and 1904 is 904400.

LCM(1900,1904) = 904400

LCM of 1900 and 1904

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

LCM of:
and

Least Common Multiple of 1900 and 1904

LCM of 1900 and 1904 is 904400

Least common multiple can be found by multiplying the highest exponent prime factors of 1900 and 1904. First we will calculate the prime factors of 1900 and 1904.

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

Prime Factorization of 1904


2 1904
2 952
2 476
2 238
7 119
17 17
1

Prime factors of 1904 are 2, 7,17. Prime factorization of 1904 in exponential form is:

1904 = 24×71×171

Now multiplying the highest exponent prime factors to calculate the LCM of 1900 and 1904.

LCM(1900,1904) = 24×52×71×171×191
LCM(1900,1904) = 904400

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

Factors of 1904

List of positive integer factors of 1904 that divides 1904 without a remainder.

1, 2, 4, 7, 8, 14, 16, 17, 28, 34, 56, 68, 112, 119, 136, 238, 272, 476, 952, 1904

Least Common Multiple of 1900 and 1904 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1900 and 1904, than apply into the LCM equation.

GCF(1900,1904) = 4
LCM(1900,1904) = ( 1900 × 1904) / 4
LCM(1900,1904) = 3617600 / 4
LCM(1900,1904) = 904400

Properties of LCM 1900 and 1904

(i) The LCM of 1904 and 1900 is associative

LCM of 1900 and 1904 = LCM of 1904 and 1900

Related Least Common Multiples of 1900

Related Least Common Multiples of 1904

Frequently Asked Questions on LCM of 1900 and 1904

1. What is the LCM of 1900 and 1904?

Answer: LCM of 1900 and 1904 is 904400.

2. 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.

3. What are the Factors of 1904?

Answer: Factors of 1904 are 1, 2, 4, 7, 8, 14, 16, 17, 28, 34, 56, 68, 112, 119, 136, 238, 272, 476, 952, 1904. There are 20 integers that are factors of 1904. The greatest factor of 1904 is 1904.

4. How to Find the LCM of 1900 and 1904?

Answer:

Least Common Multiple of 1900 and 1904 = 904400

Step 1: Find the prime factorization of 1900

1900 = 2 x 2 x 5 x 5 x 19

Step 2: Find the prime factorization of 1904

1904 = 2 x 2 x 2 x 2 x 7 x 17

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

LCM = 904400 = 2 x 2 x 2 x 2 x 5 x 5 x 7 x 17 x 19

Step 4: Therefore, the least common multiple of 1900 and 1904 is 904400.