Least Common Multiple of 1200 and 1208

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1200 and 1208 the smallest integer that is 181200 that is divisible by both numbers.

Least Common Multiple (LCM) of 1200 and 1208 is 181200.

LCM(1200,1208) = 181200

LCM of 1200 and 1208

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

LCM of:
and

Least Common Multiple of 1200 and 1208

LCM of 1200 and 1208 is 181200

Least common multiple can be found by multiplying the highest exponent prime factors of 1200 and 1208. First we will calculate the prime factors of 1200 and 1208.

Prime Factorization of 1200


2 1200
2 600
2 300
2 150
3 75
5 25
5 5
1

Prime factors of 1200 are 2, 3,5. Prime factorization of 1200 in exponential form is:

1200 = 24×31×52

Prime Factorization of 1208


2 1208
2 604
2 302
151 151
1

Prime factors of 1208 are 2,151. Prime factorization of 1208 in exponential form is:

1208 = 23×1511

Now multiplying the highest exponent prime factors to calculate the LCM of 1200 and 1208.

LCM(1200,1208) = 24×31×52×1511
LCM(1200,1208) = 181200

Factors of 1200

List of positive integer factors of 1200 that divides 1200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200

Factors of 1208

List of positive integer factors of 1208 that divides 1208 without a remainder.

1, 2, 4, 8, 151, 302, 604, 1208

Least Common Multiple of 1200 and 1208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1200 and 1208, than apply into the LCM equation.

GCF(1200,1208) = 8
LCM(1200,1208) = ( 1200 × 1208) / 8
LCM(1200,1208) = 1449600 / 8
LCM(1200,1208) = 181200

Properties of LCM 1200 and 1208

(i) The LCM of 1208 and 1200 is associative

LCM of 1200 and 1208 = LCM of 1208 and 1200

Related Least Common Multiples of 1200

Related Least Common Multiples of 1208

Frequently Asked Questions on LCM of 1200 and 1208

1. What is the LCM of 1200 and 1208?

Answer: LCM of 1200 and 1208 is 181200.

2. What are the Factors of 1200?

Answer: Factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200. There are 30 integers that are factors of 1200. The greatest factor of 1200 is 1200.

3. What are the Factors of 1208?

Answer: Factors of 1208 are 1, 2, 4, 8, 151, 302, 604, 1208. There are 8 integers that are factors of 1208. The greatest factor of 1208 is 1208.

4. How to Find the LCM of 1200 and 1208?

Answer:

Least Common Multiple of 1200 and 1208 = 181200

Step 1: Find the prime factorization of 1200

1200 = 2 x 2 x 2 x 2 x 3 x 5 x 5

Step 2: Find the prime factorization of 1208

1208 = 2 x 2 x 2 x 151

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

LCM = 181200 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 151

Step 4: Therefore, the least common multiple of 1200 and 1208 is 181200.