Least Common Multiple of 1904 and 1909

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1904 and 1909 the smallest integer that is 3634736 that is divisible by both numbers.

Least Common Multiple (LCM) of 1904 and 1909 is 3634736.

LCM(1904,1909) = 3634736

LCM of 1904 and 1909

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

LCM of:
and

Least Common Multiple of 1904 and 1909

LCM of 1904 and 1909 is 3634736

Least common multiple can be found by multiplying the highest exponent prime factors of 1904 and 1909. First we will calculate the prime factors of 1904 and 1909.

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

Prime Factorization of 1909


23 1909
83 83
1

Prime factors of 1909 are 23,83. Prime factorization of 1909 in exponential form is:

1909 = 231×831

Now multiplying the highest exponent prime factors to calculate the LCM of 1904 and 1909.

LCM(1904,1909) = 24×71×171×231×831
LCM(1904,1909) = 3634736

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

Factors of 1909

List of positive integer factors of 1909 that divides 1909 without a remainder.

1, 23, 83, 1909

Least Common Multiple of 1904 and 1909 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1904 and 1909, than apply into the LCM equation.

GCF(1904,1909) = 1
LCM(1904,1909) = ( 1904 × 1909) / 1
LCM(1904,1909) = 3634736 / 1
LCM(1904,1909) = 3634736

Properties of LCM 1904 and 1909

(i) The LCM of 1909 and 1904 is associative

LCM of 1904 and 1909 = LCM of 1909 and 1904

Related Least Common Multiples of 1904

Related Least Common Multiples of 1909

Frequently Asked Questions on LCM of 1904 and 1909

1. What is the LCM of 1904 and 1909?

Answer: LCM of 1904 and 1909 is 3634736.

2. 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.

3. What are the Factors of 1909?

Answer: Factors of 1909 are 1, 23, 83, 1909. There are 4 integers that are factors of 1909. The greatest factor of 1909 is 1909.

4. How to Find the LCM of 1904 and 1909?

Answer:

Least Common Multiple of 1904 and 1909 = 3634736

Step 1: Find the prime factorization of 1904

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

Step 2: Find the prime factorization of 1909

1909 = 23 x 83

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

LCM = 3634736 = 2 x 2 x 2 x 2 x 7 x 17 x 23 x 83

Step 4: Therefore, the least common multiple of 1904 and 1909 is 3634736.