Least Common Multiple of 1600 and 1605

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1600 and 1605 the smallest integer that is 513600 that is divisible by both numbers.

Least Common Multiple (LCM) of 1600 and 1605 is 513600.

LCM(1600,1605) = 513600

LCM of 1600 and 1605

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

LCM of:
and

Least Common Multiple of 1600 and 1605

LCM of 1600 and 1605 is 513600

Least common multiple can be found by multiplying the highest exponent prime factors of 1600 and 1605. First we will calculate the prime factors of 1600 and 1605.

Prime Factorization of 1600


2 1600
2 800
2 400
2 200
2 100
2 50
5 25
5 5
1

Prime factors of 1600 are 2,5. Prime factorization of 1600 in exponential form is:

1600 = 26×52

Prime Factorization of 1605


3 1605
5 535
107 107
1

Prime factors of 1605 are 3, 5,107. Prime factorization of 1605 in exponential form is:

1605 = 31×51×1071

Now multiplying the highest exponent prime factors to calculate the LCM of 1600 and 1605.

LCM(1600,1605) = 26×31×52×1071
LCM(1600,1605) = 513600

Factors of 1600

List of positive integer factors of 1600 that divides 1600 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600

Factors of 1605

List of positive integer factors of 1605 that divides 1605 without a remainder.

1, 3, 5, 15, 107, 321, 535, 1605

Least Common Multiple of 1600 and 1605 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1600 and 1605, than apply into the LCM equation.

GCF(1600,1605) = 5
LCM(1600,1605) = ( 1600 × 1605) / 5
LCM(1600,1605) = 2568000 / 5
LCM(1600,1605) = 513600

Properties of LCM 1600 and 1605

(i) The LCM of 1605 and 1600 is associative

LCM of 1600 and 1605 = LCM of 1605 and 1600

Related Least Common Multiples of 1600

Related Least Common Multiples of 1605

Frequently Asked Questions on LCM of 1600 and 1605

1. What is the LCM of 1600 and 1605?

Answer: LCM of 1600 and 1605 is 513600.

2. What are the Factors of 1600?

Answer: Factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600. There are 21 integers that are factors of 1600. The greatest factor of 1600 is 1600.

3. What are the Factors of 1605?

Answer: Factors of 1605 are 1, 3, 5, 15, 107, 321, 535, 1605. There are 8 integers that are factors of 1605. The greatest factor of 1605 is 1605.

4. How to Find the LCM of 1600 and 1605?

Answer:

Least Common Multiple of 1600 and 1605 = 513600

Step 1: Find the prime factorization of 1600

1600 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 1605

1605 = 3 x 5 x 107

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

LCM = 513600 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 107

Step 4: Therefore, the least common multiple of 1600 and 1605 is 513600.