Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 213 and 221 the smallest integer that is 47073 that is divisible by both numbers.
Least Common Multiple (LCM) of 213 and 221 is 47073.
LCM(213,221) = 47073
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 213 and 221. First we will calculate the prime factors of 213 and 221.
Prime Factorization of 213
3 | 213 |
71 | 71 |
1 |
Prime factors of 213 are 3,71. Prime factorization of 213 in exponential form is:
213 = 31×711
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 213 and 221.
LCM(213,221) = 31×131×171×711
LCM(213,221) = 47073
Factors of 213
List of positive integer factors of 213 that divides 213 without a remainder.
1, 3, 71, 213
Factors of 221
List of positive integer factors of 221 that divides 221 without a remainder.
1, 13, 17, 221
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 213 and 221, than apply into the LCM equation.
GCF(213,221) = 1
LCM(213,221) = ( 213 × 221) / 1
LCM(213,221) = 47073 / 1
LCM(213,221) = 47073
(i) The LCM of 221 and 213 is associative
LCM of 213 and 221 = LCM of 221 and 213
1. What is the LCM of 213 and 221?
Answer: LCM of 213 and 221 is 47073.
2. What are the Factors of 213?
Answer: Factors of 213 are 1, 3, 71, 213. There are 4 integers that are factors of 213. The greatest factor of 213 is 213.
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 213 and 221?
Answer:
Least Common Multiple of 213 and 221 = 47073
Step 1: Find the prime factorization of 213
213 = 3 x 71
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 = 47073 = 3 x 13 x 17 x 71
Step 4: Therefore, the least common multiple of 213 and 221 is 47073.