Least Common Multiple of 345 and 350
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 345 and 350 the smallest integer that is 24150 that is divisible by both numbers.
Least Common Multiple (LCM) of 345 and 350 is 24150.
LCM(345,350) = 24150
LCM of 345 and 350
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 345 and 350 by Prime method
- Least Common Multiple of 345 and 350 with GCF Formula
LCM of 345 and 350 is 24150
Least common multiple can be found by multiplying the highest exponent prime factors of 345 and 350. First we will calculate the prime factors of 345 and 350.
Prime Factorization of 345
| 3 | 345 |
| 5 | 115 |
| 23 | 23 |
| 1 |
Prime factors of 345 are 3, 5,23. Prime factorization of 345 in exponential form is:
345 = 31×51×231
Prime Factorization of 350
| 2 | 350 |
| 5 | 175 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 350 are 2, 5,7. Prime factorization of 350 in exponential form is:
350 = 21×52×71
Now multiplying the highest exponent prime factors to calculate the LCM of 345 and 350.
LCM(345,350) = 21×31×52×71×231
LCM(345,350) = 24150
Factors of 345
List of positive integer factors of 345 that divides 345 without a remainder.
1, 3, 5, 15, 23, 69, 115, 345
Factors of 350
List of positive integer factors of 350 that divides 350 without a remainder.
1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
Least Common Multiple of 345 and 350 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 345 and 350, than apply into the LCM equation.
GCF(345,350) = 5
LCM(345,350) = ( 345 × 350) / 5
LCM(345,350) = 120750 / 5
LCM(345,350) = 24150
Properties of LCM 345 and 350
(i) The LCM of 350 and 345 is associative
LCM of 345 and 350 = LCM of 350 and 345
Related Least Common Multiples of 345
Related Least Common Multiples of 350
Frequently Asked Questions on LCM of 345 and 350
1. What is the LCM of 345 and 350?
Answer: LCM of 345 and 350 is 24150.
2. What are the Factors of 345?
Answer: Factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345. There are 8 integers that are factors of 345. The greatest factor of 345 is 345.
3. What are the Factors of 350?
Answer: Factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350. There are 12 integers that are factors of 350. The greatest factor of 350 is 350.
4. How to Find the LCM of 345 and 350?
Answer:
Least Common Multiple of 345 and 350 = 24150
Step 1: Find the prime factorization of 345
345 = 3 x 5 x 23
Step 2: Find the prime factorization of 350
350 = 2 x 5 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 = 24150 = 2 x 3 x 5 x 5 x 7 x 23
Step 4: Therefore, the least common multiple of 345 and 350 is 24150.