Least Common Multiple of 600 and 1050

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 600 and 1050 the smallest integer that is 4200 that is divisible by both numbers.

Least Common Multiple (LCM) of 600 and 1050 is 4200.

LCM(600,1050) = 4200

LCM of 600 and 1050

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

LCM of:
and

Least Common Multiple of 600 and 1050

LCM of 600 and 1050 is 4200

Least common multiple can be found by multiplying the highest exponent prime factors of 600 and 1050. First we will calculate the prime factors of 600 and 1050.

Prime Factorization of 600


2 600
2 300
2 150
3 75
5 25
5 5
1

Prime factors of 600 are 2, 3,5. Prime factorization of 600 in exponential form is:

600 = 23×31×52

Prime Factorization of 1050


2 1050
3 525
5 175
5 35
7 7
1

Prime factors of 1050 are 2, 3, 5,7. Prime factorization of 1050 in exponential form is:

1050 = 21×31×52×71

Now multiplying the highest exponent prime factors to calculate the LCM of 600 and 1050.

LCM(600,1050) = 23×31×52×71
LCM(600,1050) = 4200

Factors of 600

List of positive integer factors of 600 that divides 600 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600

Factors of 1050

List of positive integer factors of 1050 that divides 1050 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050

Least Common Multiple of 600 and 1050 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 600 and 1050, than apply into the LCM equation.

GCF(600,1050) = 150
LCM(600,1050) = ( 600 × 1050) / 150
LCM(600,1050) = 630000 / 150
LCM(600,1050) = 4200

Properties of LCM 600 and 1050

(i) The LCM of 1050 and 600 is associative

LCM of 600 and 1050 = LCM of 1050 and 600

Related Least Common Multiples of 600

Related Least Common Multiples of 1050

Frequently Asked Questions on LCM of 600 and 1050

1. What is the LCM of 600 and 1050?

Answer: LCM of 600 and 1050 is 4200.

2. What are the Factors of 600?

Answer: Factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600. There are 24 integers that are factors of 600. The greatest factor of 600 is 600.

3. What are the Factors of 1050?

Answer: Factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050. There are 24 integers that are factors of 1050. The greatest factor of 1050 is 1050.

4. How to Find the LCM of 600 and 1050?

Answer:

Least Common Multiple of 600 and 1050 = 4200

Step 1: Find the prime factorization of 600

600 = 2 x 2 x 2 x 3 x 5 x 5

Step 2: Find the prime factorization of 1050

1050 = 2 x 3 x 5 x 5 x 7

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

LCM = 4200 = 2 x 2 x 2 x 3 x 5 x 5 x 7

Step 4: Therefore, the least common multiple of 600 and 1050 is 4200.