Least Common Multiple of 315 and 322
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 315 and 322 the smallest integer that is 14490 that is divisible by both numbers.
Least Common Multiple (LCM) of 315 and 322 is 14490.
LCM(315,322) = 14490
LCM of 315 and 322
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 315 and 322 by Prime method
- Least Common Multiple of 315 and 322 with GCF Formula
LCM of 315 and 322 is 14490
Least common multiple can be found by multiplying the highest exponent prime factors of 315 and 322. First we will calculate the prime factors of 315 and 322.
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
Prime Factorization of 322
| 2 | 322 |
| 7 | 161 |
| 23 | 23 |
| 1 |
Prime factors of 322 are 2, 7,23. Prime factorization of 322 in exponential form is:
322 = 21×71×231
Now multiplying the highest exponent prime factors to calculate the LCM of 315 and 322.
LCM(315,322) = 21×32×51×71×231
LCM(315,322) = 14490
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
Factors of 322
List of positive integer factors of 322 that divides 322 without a remainder.
1, 2, 7, 14, 23, 46, 161, 322
Least Common Multiple of 315 and 322 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 315 and 322, than apply into the LCM equation.
GCF(315,322) = 7
LCM(315,322) = ( 315 × 322) / 7
LCM(315,322) = 101430 / 7
LCM(315,322) = 14490
Properties of LCM 315 and 322
(i) The LCM of 322 and 315 is associative
LCM of 315 and 322 = LCM of 322 and 315
Related Least Common Multiples of 315
Related Least Common Multiples of 322
Frequently Asked Questions on LCM of 315 and 322
1. What is the LCM of 315 and 322?
Answer: LCM of 315 and 322 is 14490.
2. 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.
3. What are the Factors of 322?
Answer: Factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322. There are 8 integers that are factors of 322. The greatest factor of 322 is 322.
4. How to Find the LCM of 315 and 322?
Answer:
Least Common Multiple of 315 and 322 = 14490
Step 1: Find the prime factorization of 315
315 = 3 x 3 x 5 x 7
Step 2: Find the prime factorization of 322
322 = 2 x 7 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 14490 = 2 x 3 x 3 x 5 x 7 x 23
Step 4: Therefore, the least common multiple of 315 and 322 is 14490.
