Least Common Multiple of 202 and 208

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 202 and 208 the smallest integer that is 21008 that is divisible by both numbers.

Least Common Multiple (LCM) of 202 and 208 is 21008.

LCM(202,208) = 21008

LCM of 202 and 208

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

LCM of:
and

Least Common Multiple of 202 and 208

LCM of 202 and 208 is 21008

Least common multiple can be found by multiplying the highest exponent prime factors of 202 and 208. First we will calculate the prime factors of 202 and 208.

Prime Factorization of 202


2 202
101 101
1

Prime factors of 202 are 2,101. Prime factorization of 202 in exponential form is:

202 = 21×1011

Prime Factorization of 208


2 208
2 104
2 52
2 26
13 13
1

Prime factors of 208 are 2,13. Prime factorization of 208 in exponential form is:

208 = 24×131

Now multiplying the highest exponent prime factors to calculate the LCM of 202 and 208.

LCM(202,208) = 24×131×1011
LCM(202,208) = 21008

Factors of 202

List of positive integer factors of 202 that divides 202 without a remainder.

1, 2, 101, 202

Factors of 208

List of positive integer factors of 208 that divides 208 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 208

Least Common Multiple of 202 and 208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 202 and 208, than apply into the LCM equation.

GCF(202,208) = 2
LCM(202,208) = ( 202 × 208) / 2
LCM(202,208) = 42016 / 2
LCM(202,208) = 21008

Properties of LCM 202 and 208

(i) The LCM of 208 and 202 is associative

LCM of 202 and 208 = LCM of 208 and 202

Related Least Common Multiples of 202

Related Least Common Multiples of 208

Frequently Asked Questions on LCM of 202 and 208

1. What is the LCM of 202 and 208?

Answer: LCM of 202 and 208 is 21008.

2. What are the Factors of 202?

Answer: Factors of 202 are 1, 2, 101, 202. There are 4 integers that are factors of 202. The greatest factor of 202 is 202.

3. What are the Factors of 208?

Answer: Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. There are 10 integers that are factors of 208. The greatest factor of 208 is 208.

4. How to Find the LCM of 202 and 208?

Answer:

Least Common Multiple of 202 and 208 = 21008

Step 1: Find the prime factorization of 202

202 = 2 x 101

Step 2: Find the prime factorization of 208

208 = 2 x 2 x 2 x 2 x 13

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

LCM = 21008 = 2 x 2 x 2 x 2 x 13 x 101

Step 4: Therefore, the least common multiple of 202 and 208 is 21008.