Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 210 and 213 the smallest integer that is 14910 that is divisible by both numbers.
Least Common Multiple (LCM) of 210 and 213 is 14910.
LCM(210,213) = 14910
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 210 and 213. First we will calculate the prime factors of 210 and 213.
Prime Factorization of 210
2 | 210 |
3 | 105 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 210 are 2, 3, 5,7. Prime factorization of 210 in exponential form is:
210 = 21×31×51×71
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
Now multiplying the highest exponent prime factors to calculate the LCM of 210 and 213.
LCM(210,213) = 21×31×51×71×711
LCM(210,213) = 14910
Factors of 210
List of positive integer factors of 210 that divides 210 without a remainder.
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Factors of 213
List of positive integer factors of 213 that divides 213 without a remainder.
1, 3, 71, 213
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 210 and 213, than apply into the LCM equation.
GCF(210,213) = 3
LCM(210,213) = ( 210 × 213) / 3
LCM(210,213) = 44730 / 3
LCM(210,213) = 14910
(i) The LCM of 213 and 210 is associative
LCM of 210 and 213 = LCM of 213 and 210
1. What is the LCM of 210 and 213?
Answer: LCM of 210 and 213 is 14910.
2. What are the Factors of 210?
Answer: Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210. There are 16 integers that are factors of 210. The greatest factor of 210 is 210.
3. 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.
4. How to Find the LCM of 210 and 213?
Answer:
Least Common Multiple of 210 and 213 = 14910
Step 1: Find the prime factorization of 210
210 = 2 x 3 x 5 x 7
Step 2: Find the prime factorization of 213
213 = 3 x 71
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 14910 = 2 x 3 x 5 x 7 x 71
Step 4: Therefore, the least common multiple of 210 and 213 is 14910.