Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 610 and 614 the smallest integer that is 187270 that is divisible by both numbers.
Least Common Multiple (LCM) of 610 and 614 is 187270.
LCM(610,614) = 187270
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 610 and 614. First we will calculate the prime factors of 610 and 614.
Prime Factorization of 610
2 | 610 |
5 | 305 |
61 | 61 |
1 |
Prime factors of 610 are 2, 5,61. Prime factorization of 610 in exponential form is:
610 = 21×51×611
Prime Factorization of 614
2 | 614 |
307 | 307 |
1 |
Prime factors of 614 are 2,307. Prime factorization of 614 in exponential form is:
614 = 21×3071
Now multiplying the highest exponent prime factors to calculate the LCM of 610 and 614.
LCM(610,614) = 21×51×611×3071
LCM(610,614) = 187270
Factors of 610
List of positive integer factors of 610 that divides 610 without a remainder.
1, 2, 5, 10, 61, 122, 305, 610
Factors of 614
List of positive integer factors of 614 that divides 614 without a remainder.
1, 2, 307, 614
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 610 and 614, than apply into the LCM equation.
GCF(610,614) = 2
LCM(610,614) = ( 610 × 614) / 2
LCM(610,614) = 374540 / 2
LCM(610,614) = 187270
(i) The LCM of 614 and 610 is associative
LCM of 610 and 614 = LCM of 614 and 610
1. What is the LCM of 610 and 614?
Answer: LCM of 610 and 614 is 187270.
2. What are the Factors of 610?
Answer: Factors of 610 are 1, 2, 5, 10, 61, 122, 305, 610. There are 8 integers that are factors of 610. The greatest factor of 610 is 610.
3. What are the Factors of 614?
Answer: Factors of 614 are 1, 2, 307, 614. There are 4 integers that are factors of 614. The greatest factor of 614 is 614.
4. How to Find the LCM of 610 and 614?
Answer:
Least Common Multiple of 610 and 614 = 187270
Step 1: Find the prime factorization of 610
610 = 2 x 5 x 61
Step 2: Find the prime factorization of 614
614 = 2 x 307
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 187270 = 2 x 5 x 61 x 307
Step 4: Therefore, the least common multiple of 610 and 614 is 187270.