Least Common Multiple of 310 and 315
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 310 and 315 the smallest integer that is 19530 that is divisible by both numbers.
Least Common Multiple (LCM) of 310 and 315 is 19530.
LCM(310,315) = 19530
LCM of 310 and 315
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 310 and 315 by Prime method
- Least Common Multiple of 310 and 315 with GCF Formula
LCM of 310 and 315 is 19530
Least common multiple can be found by multiplying the highest exponent prime factors of 310 and 315. First we will calculate the prime factors of 310 and 315.
Prime Factorization of 310
| 2 | 310 |
| 5 | 155 |
| 31 | 31 |
| 1 |
Prime factors of 310 are 2, 5,31. Prime factorization of 310 in exponential form is:
310 = 21×51×311
Prime Factorization of 315
| 3 | 315 |
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 315 are 3, 5,7. Prime factorization of 315 in exponential form is:
315 = 32×51×71
Now multiplying the highest exponent prime factors to calculate the LCM of 310 and 315.
LCM(310,315) = 21×32×51×71×311
LCM(310,315) = 19530
Factors of 310
List of positive integer factors of 310 that divides 310 without a remainder.
1, 2, 5, 10, 31, 62, 155, 310
Factors of 315
List of positive integer factors of 315 that divides 315 without a remainder.
1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
Least Common Multiple of 310 and 315 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 310 and 315, than apply into the LCM equation.
GCF(310,315) = 5
LCM(310,315) = ( 310 × 315) / 5
LCM(310,315) = 97650 / 5
LCM(310,315) = 19530
Properties of LCM 310 and 315
(i) The LCM of 315 and 310 is associative
LCM of 310 and 315 = LCM of 315 and 310
Related Least Common Multiples of 310
Related Least Common Multiples of 315
Frequently Asked Questions on LCM of 310 and 315
1. What is the LCM of 310 and 315?
Answer: LCM of 310 and 315 is 19530.
2. What are the Factors of 310?
Answer: Factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310. There are 8 integers that are factors of 310. The greatest factor of 310 is 310.
3. What are the Factors of 315?
Answer: Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. There are 12 integers that are factors of 315. The greatest factor of 315 is 315.
4. How to Find the LCM of 310 and 315?
Answer:
Least Common Multiple of 310 and 315 = 19530
Step 1: Find the prime factorization of 310
310 = 2 x 5 x 31
Step 2: Find the prime factorization of 315
315 = 3 x 3 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 19530 = 2 x 3 x 3 x 5 x 7 x 31
Step 4: Therefore, the least common multiple of 310 and 315 is 19530.