Least Common Multiple of 214 and 221
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 221 the smallest integer that is 47294 that is divisible by both numbers.
Least Common Multiple (LCM) of 214 and 221 is 47294.
LCM(214,221) = 47294
LCM of 214 and 221
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 214 and 221 by Prime method
- Least Common Multiple of 214 and 221 with GCF Formula
LCM of 214 and 221 is 47294
Least common multiple can be found by multiplying the highest exponent prime factors of 214 and 221. First we will calculate the prime factors of 214 and 221.
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 221
| 13 | 221 |
| 17 | 17 |
| 1 |
Prime factors of 221 are 13,17. Prime factorization of 221 in exponential form is:
221 = 131×171
Now multiplying the highest exponent prime factors to calculate the LCM of 214 and 221.
LCM(214,221) = 21×131×171×1071
LCM(214,221) = 47294
Factors of 214
List of positive integer factors of 214 that divides 214 without a remainder.
1, 2, 107, 214
Factors of 221
List of positive integer factors of 221 that divides 221 without a remainder.
1, 13, 17, 221
Least Common Multiple of 214 and 221 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 221, than apply into the LCM equation.
GCF(214,221) = 1
LCM(214,221) = ( 214 × 221) / 1
LCM(214,221) = 47294 / 1
LCM(214,221) = 47294
Properties of LCM 214 and 221
(i) The LCM of 221 and 214 is associative
LCM of 214 and 221 = LCM of 221 and 214
Related Least Common Multiples of 214
Related Least Common Multiples of 221
Frequently Asked Questions on LCM of 214 and 221
1. What is the LCM of 214 and 221?
Answer: LCM of 214 and 221 is 47294.
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 221?
Answer: Factors of 221 are 1, 13, 17, 221. There are 4 integers that are factors of 221. The greatest factor of 221 is 221.
4. How to Find the LCM of 214 and 221?
Answer:
Least Common Multiple of 214 and 221 = 47294
Step 1: Find the prime factorization of 214
214 = 2 x 107
Step 2: Find the prime factorization of 221
221 = 13 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 47294 = 2 x 13 x 17 x 107
Step 4: Therefore, the least common multiple of 214 and 221 is 47294.
