Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 17210 and 17214 the smallest integer that is 148126470 that is divisible by both numbers.
Least Common Multiple (LCM) of 17210 and 17214 is 148126470.
LCM(17210,17214) = 148126470
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 17210 and 17214. First we will calculate the prime factors of 17210 and 17214.
Prime Factorization of 17210
2 | 17210 |
5 | 8605 |
1721 | 1721 |
1 |
Prime factors of 17210 are 2, 5,1721. Prime factorization of 17210 in exponential form is:
17210 = 21×51×17211
Prime Factorization of 17214
2 | 17214 |
3 | 8607 |
19 | 2869 |
151 | 151 |
1 |
Prime factors of 17214 are 2, 3, 19,151. Prime factorization of 17214 in exponential form is:
17214 = 21×31×191×1511
Now multiplying the highest exponent prime factors to calculate the LCM of 17210 and 17214.
LCM(17210,17214) = 21×31×51×191×1511×17211
LCM(17210,17214) = 148126470
Factors of 17210
List of positive integer factors of 17210 that divides 17210 without a remainder.
1, 2, 5, 10, 1721, 3442, 8605, 17210
Factors of 17214
List of positive integer factors of 17214 that divides 17214 without a remainder.
1, 2, 3, 6, 19, 38, 57, 114, 151, 302, 453, 906, 2869, 5738, 8607, 17214
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17210 and 17214, than apply into the LCM equation.
GCF(17210,17214) = 2
LCM(17210,17214) = ( 17210 × 17214) / 2
LCM(17210,17214) = 296252940 / 2
LCM(17210,17214) = 148126470
(i) The LCM of 17214 and 17210 is associative
LCM of 17210 and 17214 = LCM of 17214 and 17210
1. What is the LCM of 17210 and 17214?
Answer: LCM of 17210 and 17214 is 148126470.
2. What are the Factors of 17210?
Answer: Factors of 17210 are 1, 2, 5, 10, 1721, 3442, 8605, 17210. There are 8 integers that are factors of 17210. The greatest factor of 17210 is 17210.
3. What are the Factors of 17214?
Answer: Factors of 17214 are 1, 2, 3, 6, 19, 38, 57, 114, 151, 302, 453, 906, 2869, 5738, 8607, 17214. There are 16 integers that are factors of 17214. The greatest factor of 17214 is 17214.
4. How to Find the LCM of 17210 and 17214?
Answer:
Least Common Multiple of 17210 and 17214 = 148126470
Step 1: Find the prime factorization of 17210
17210 = 2 x 5 x 1721
Step 2: Find the prime factorization of 17214
17214 = 2 x 3 x 19 x 151
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 148126470 = 2 x 3 x 5 x 19 x 151 x 1721
Step 4: Therefore, the least common multiple of 17210 and 17214 is 148126470.