Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1210 and 1214 the smallest integer that is 734470 that is divisible by both numbers.
Least Common Multiple (LCM) of 1210 and 1214 is 734470.
LCM(1210,1214) = 734470
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 1210 and 1214. First we will calculate the prime factors of 1210 and 1214.
Prime Factorization of 1210
2 | 1210 |
5 | 605 |
11 | 121 |
11 | 11 |
1 |
Prime factors of 1210 are 2, 5,11. Prime factorization of 1210 in exponential form is:
1210 = 21×51×112
Prime Factorization of 1214
2 | 1214 |
607 | 607 |
1 |
Prime factors of 1214 are 2,607. Prime factorization of 1214 in exponential form is:
1214 = 21×6071
Now multiplying the highest exponent prime factors to calculate the LCM of 1210 and 1214.
LCM(1210,1214) = 21×51×112×6071
LCM(1210,1214) = 734470
Factors of 1210
List of positive integer factors of 1210 that divides 1210 without a remainder.
1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210
Factors of 1214
List of positive integer factors of 1214 that divides 1214 without a remainder.
1, 2, 607, 1214
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1210 and 1214, than apply into the LCM equation.
GCF(1210,1214) = 2
LCM(1210,1214) = ( 1210 × 1214) / 2
LCM(1210,1214) = 1468940 / 2
LCM(1210,1214) = 734470
(i) The LCM of 1214 and 1210 is associative
LCM of 1210 and 1214 = LCM of 1214 and 1210
1. What is the LCM of 1210 and 1214?
Answer: LCM of 1210 and 1214 is 734470.
2. What are the Factors of 1210?
Answer: Factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210. There are 12 integers that are factors of 1210. The greatest factor of 1210 is 1210.
3. What are the Factors of 1214?
Answer: Factors of 1214 are 1, 2, 607, 1214. There are 4 integers that are factors of 1214. The greatest factor of 1214 is 1214.
4. How to Find the LCM of 1210 and 1214?
Answer:
Least Common Multiple of 1210 and 1214 = 734470
Step 1: Find the prime factorization of 1210
1210 = 2 x 5 x 11 x 11
Step 2: Find the prime factorization of 1214
1214 = 2 x 607
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 734470 = 2 x 5 x 11 x 11 x 607
Step 4: Therefore, the least common multiple of 1210 and 1214 is 734470.