Least Common Multiple of 214 and 217

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 217 the smallest integer that is 46438 that is divisible by both numbers.

Least Common Multiple (LCM) of 214 and 217 is 46438.

LCM(214,217) = 46438

LCM of 214 and 217

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

LCM of:
and

Least Common Multiple of 214 and 217

LCM of 214 and 217 is 46438

Least common multiple can be found by multiplying the highest exponent prime factors of 214 and 217. First we will calculate the prime factors of 214 and 217.

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 217


7 217
31 31
1

Prime factors of 217 are 7,31. Prime factorization of 217 in exponential form is:

217 = 71×311

Now multiplying the highest exponent prime factors to calculate the LCM of 214 and 217.

LCM(214,217) = 21×71×311×1071
LCM(214,217) = 46438

Factors of 214

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

1, 2, 107, 214

Factors of 217

List of positive integer factors of 217 that divides 217 without a remainder.

1, 7, 31, 217

Least Common Multiple of 214 and 217 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 217, than apply into the LCM equation.

GCF(214,217) = 1
LCM(214,217) = ( 214 × 217) / 1
LCM(214,217) = 46438 / 1
LCM(214,217) = 46438

Properties of LCM 214 and 217

(i) The LCM of 217 and 214 is associative

LCM of 214 and 217 = LCM of 217 and 214

Related Least Common Multiples of 214

Related Least Common Multiples of 217

Frequently Asked Questions on LCM of 214 and 217

1. What is the LCM of 214 and 217?

Answer: LCM of 214 and 217 is 46438.

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 217?

Answer: Factors of 217 are 1, 7, 31, 217. There are 4 integers that are factors of 217. The greatest factor of 217 is 217.

4. How to Find the LCM of 214 and 217?

Answer:

Least Common Multiple of 214 and 217 = 46438

Step 1: Find the prime factorization of 214

214 = 2 x 107

Step 2: Find the prime factorization of 217

217 = 7 x 31

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

LCM = 46438 = 2 x 7 x 31 x 107

Step 4: Therefore, the least common multiple of 214 and 217 is 46438.