Least Common Multiple of 1208 and 1214

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1208 and 1214 the smallest integer that is 733256 that is divisible by both numbers.

Least Common Multiple (LCM) of 1208 and 1214 is 733256.

LCM(1208,1214) = 733256

LCM of 1208 and 1214

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

LCM of:
and

Least Common Multiple of 1208 and 1214

LCM of 1208 and 1214 is 733256

Least common multiple can be found by multiplying the highest exponent prime factors of 1208 and 1214. First we will calculate the prime factors of 1208 and 1214.

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

Prime Factorization of 1214


2 1214
607 607
1

Prime factors of 1214 are 2,607. Prime factorization of 1214 in exponential form is:

1214 = 21×6071

Now multiplying the highest exponent prime factors to calculate the LCM of 1208 and 1214.

LCM(1208,1214) = 23×1511×6071
LCM(1208,1214) = 733256

Factors of 1208

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

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

Factors of 1214

List of positive integer factors of 1214 that divides 1214 without a remainder.

1, 2, 607, 1214

Least Common Multiple of 1208 and 1214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1208 and 1214, than apply into the LCM equation.

GCF(1208,1214) = 2
LCM(1208,1214) = ( 1208 × 1214) / 2
LCM(1208,1214) = 1466512 / 2
LCM(1208,1214) = 733256

Properties of LCM 1208 and 1214

(i) The LCM of 1214 and 1208 is associative

LCM of 1208 and 1214 = LCM of 1214 and 1208

Related Least Common Multiples of 1208

Related Least Common Multiples of 1214

Frequently Asked Questions on LCM of 1208 and 1214

1. What is the LCM of 1208 and 1214?

Answer: LCM of 1208 and 1214 is 733256.

2. 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.

3. What are the Factors of 1214?

Answer: Factors of 1214 are 1, 2, 607, 1214. There are 4 integers that are factors of 1214. The greatest factor of 1214 is 1214.

4. How to Find the LCM of 1208 and 1214?

Answer:

Least Common Multiple of 1208 and 1214 = 733256

Step 1: Find the prime factorization of 1208

1208 = 2 x 2 x 2 x 151

Step 2: Find the prime factorization of 1214

1214 = 2 x 607

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

LCM = 733256 = 2 x 2 x 2 x 151 x 607

Step 4: Therefore, the least common multiple of 1208 and 1214 is 733256.