Least Common Multiple of 3900 and 3904

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3900 and 3904 the smallest integer that is 3806400 that is divisible by both numbers.

Least Common Multiple (LCM) of 3900 and 3904 is 3806400.

LCM(3900,3904) = 3806400

LCM of 3900 and 3904

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

LCM of:
and

Least Common Multiple of 3900 and 3904

LCM of 3900 and 3904 is 3806400

Least common multiple can be found by multiplying the highest exponent prime factors of 3900 and 3904. First we will calculate the prime factors of 3900 and 3904.

Prime Factorization of 3900


2 3900
2 1950
3 975
5 325
5 65
13 13
1

Prime factors of 3900 are 2, 3, 5,13. Prime factorization of 3900 in exponential form is:

3900 = 22×31×52×131

Prime Factorization of 3904


2 3904
2 1952
2 976
2 488
2 244
2 122
61 61
1

Prime factors of 3904 are 2,61. Prime factorization of 3904 in exponential form is:

3904 = 26×611

Now multiplying the highest exponent prime factors to calculate the LCM of 3900 and 3904.

LCM(3900,3904) = 26×31×52×131×611
LCM(3900,3904) = 3806400

Factors of 3900

List of positive integer factors of 3900 that divides 3900 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 25, 26, 30, 39, 50, 52, 60, 65, 75, 78, 100, 130, 150, 156, 195, 260, 300, 325, 390, 650, 780, 975, 1300, 1950, 3900

Factors of 3904

List of positive integer factors of 3904 that divides 3904 without a remainder.

1, 2, 4, 8, 16, 32, 61, 64, 122, 244, 488, 976, 1952, 3904

Least Common Multiple of 3900 and 3904 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3900 and 3904, than apply into the LCM equation.

GCF(3900,3904) = 4
LCM(3900,3904) = ( 3900 × 3904) / 4
LCM(3900,3904) = 15225600 / 4
LCM(3900,3904) = 3806400

Properties of LCM 3900 and 3904

(i) The LCM of 3904 and 3900 is associative

LCM of 3900 and 3904 = LCM of 3904 and 3900

Related Least Common Multiples of 3900

Related Least Common Multiples of 3904

Frequently Asked Questions on LCM of 3900 and 3904

1. What is the LCM of 3900 and 3904?

Answer: LCM of 3900 and 3904 is 3806400.

2. What are the Factors of 3900?

Answer: Factors of 3900 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 25, 26, 30, 39, 50, 52, 60, 65, 75, 78, 100, 130, 150, 156, 195, 260, 300, 325, 390, 650, 780, 975, 1300, 1950, 3900. There are 36 integers that are factors of 3900. The greatest factor of 3900 is 3900.

3. What are the Factors of 3904?

Answer: Factors of 3904 are 1, 2, 4, 8, 16, 32, 61, 64, 122, 244, 488, 976, 1952, 3904. There are 14 integers that are factors of 3904. The greatest factor of 3904 is 3904.

4. How to Find the LCM of 3900 and 3904?

Answer:

Least Common Multiple of 3900 and 3904 = 3806400

Step 1: Find the prime factorization of 3900

3900 = 2 x 2 x 3 x 5 x 5 x 13

Step 2: Find the prime factorization of 3904

3904 = 2 x 2 x 2 x 2 x 2 x 2 x 61

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

LCM = 3806400 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 13 x 61

Step 4: Therefore, the least common multiple of 3900 and 3904 is 3806400.