Least Common Multiple of 214 and 220

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 214 and 220 the smallest integer that is 23540 that is divisible by both numbers.

Least Common Multiple (LCM) of 214 and 220 is 23540.

LCM(214,220) = 23540

LCM of 214 and 220

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

LCM of:
and

Least Common Multiple of 214 and 220

LCM of 214 and 220 is 23540

Least common multiple can be found by multiplying the highest exponent prime factors of 214 and 220. First we will calculate the prime factors of 214 and 220.

Prime Factorization of 214


2 214
107 107
1

Prime factors of 214 are 2,107. Prime factorization of 214 in exponential form is:

214 = 21×1071

Prime Factorization of 220


2 220
2 110
5 55
11 11
1

Prime factors of 220 are 2, 5,11. Prime factorization of 220 in exponential form is:

220 = 22×51×111

Now multiplying the highest exponent prime factors to calculate the LCM of 214 and 220.

LCM(214,220) = 22×51×111×1071
LCM(214,220) = 23540

Factors of 214

List of positive integer factors of 214 that divides 214 without a remainder.

1, 2, 107, 214

Factors of 220

List of positive integer factors of 220 that divides 220 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220

Least Common Multiple of 214 and 220 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 214 and 220, than apply into the LCM equation.

GCF(214,220) = 2
LCM(214,220) = ( 214 × 220) / 2
LCM(214,220) = 47080 / 2
LCM(214,220) = 23540

Properties of LCM 214 and 220

(i) The LCM of 220 and 214 is associative

LCM of 214 and 220 = LCM of 220 and 214

Related Least Common Multiples of 214

Related Least Common Multiples of 220

Frequently Asked Questions on LCM of 214 and 220

1. What is the LCM of 214 and 220?

Answer: LCM of 214 and 220 is 23540.

2. What are the Factors of 214?

Answer: Factors of 214 are 1, 2, 107, 214. There are 4 integers that are factors of 214. The greatest factor of 214 is 214.

3. What are the Factors of 220?

Answer: Factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220. There are 12 integers that are factors of 220. The greatest factor of 220 is 220.

4. How to Find the LCM of 214 and 220?

Answer:

Least Common Multiple of 214 and 220 = 23540

Step 1: Find the prime factorization of 214

214 = 2 x 107

Step 2: Find the prime factorization of 220

220 = 2 x 2 x 5 x 11

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

LCM = 23540 = 2 x 2 x 5 x 11 x 107

Step 4: Therefore, the least common multiple of 214 and 220 is 23540.