Least Common Multiple of 1600 and 1608

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 1608 the smallest integer that is 321600 that is divisible by both numbers.

Least Common Multiple (LCM) of 1600 and 1608 is 321600.

LCM(1600,1608) = 321600

LCM of 1600 and 1608

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

LCM of:
and

Least Common Multiple of 1600 and 1608

LCM of 1600 and 1608 is 321600

Least common multiple can be found by multiplying the highest exponent prime factors of 1600 and 1608. First we will calculate the prime factors of 1600 and 1608.

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 1608


2 1608
2 804
2 402
3 201
67 67
1

Prime factors of 1608 are 2, 3,67. Prime factorization of 1608 in exponential form is:

1608 = 23×31×671

Now multiplying the highest exponent prime factors to calculate the LCM of 1600 and 1608.

LCM(1600,1608) = 26×31×52×671
LCM(1600,1608) = 321600

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 1608

List of positive integer factors of 1608 that divides 1608 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 67, 134, 201, 268, 402, 536, 804, 1608

Least Common Multiple of 1600 and 1608 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 1608, than apply into the LCM equation.

GCF(1600,1608) = 8
LCM(1600,1608) = ( 1600 × 1608) / 8
LCM(1600,1608) = 2572800 / 8
LCM(1600,1608) = 321600

Properties of LCM 1600 and 1608

(i) The LCM of 1608 and 1600 is associative

LCM of 1600 and 1608 = LCM of 1608 and 1600

Related Least Common Multiples of 1600

Related Least Common Multiples of 1608

Frequently Asked Questions on LCM of 1600 and 1608

1. What is the LCM of 1600 and 1608?

Answer: LCM of 1600 and 1608 is 321600.

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 1608?

Answer: Factors of 1608 are 1, 2, 3, 4, 6, 8, 12, 24, 67, 134, 201, 268, 402, 536, 804, 1608. There are 16 integers that are factors of 1608. The greatest factor of 1608 is 1608.

4. How to Find the LCM of 1600 and 1608?

Answer:

Least Common Multiple of 1600 and 1608 = 321600

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 1608

1608 = 2 x 2 x 2 x 3 x 67

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

LCM = 321600 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 67

Step 4: Therefore, the least common multiple of 1600 and 1608 is 321600.