Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 350 and 357 the smallest integer that is 17850 that is divisible by both numbers.
Least Common Multiple (LCM) of 350 and 357 is 17850.
LCM(350,357) = 17850
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 350 and 357. First we will calculate the prime factors of 350 and 357.
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
Prime Factorization of 357
3 | 357 |
7 | 119 |
17 | 17 |
1 |
Prime factors of 357 are 3, 7,17. Prime factorization of 357 in exponential form is:
357 = 31×71×171
Now multiplying the highest exponent prime factors to calculate the LCM of 350 and 357.
LCM(350,357) = 21×31×52×71×171
LCM(350,357) = 17850
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
Factors of 357
List of positive integer factors of 357 that divides 357 without a remainder.
1, 3, 7, 17, 21, 51, 119, 357
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 350 and 357, than apply into the LCM equation.
GCF(350,357) = 7
LCM(350,357) = ( 350 × 357) / 7
LCM(350,357) = 124950 / 7
LCM(350,357) = 17850
(i) The LCM of 357 and 350 is associative
LCM of 350 and 357 = LCM of 357 and 350
1. What is the LCM of 350 and 357?
Answer: LCM of 350 and 357 is 17850.
2. 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.
3. What are the Factors of 357?
Answer: Factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357. There are 8 integers that are factors of 357. The greatest factor of 357 is 357.
4. How to Find the LCM of 350 and 357?
Answer:
Least Common Multiple of 350 and 357 = 17850
Step 1: Find the prime factorization of 350
350 = 2 x 5 x 5 x 7
Step 2: Find the prime factorization of 357
357 = 3 x 7 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 17850 = 2 x 3 x 5 x 5 x 7 x 17
Step 4: Therefore, the least common multiple of 350 and 357 is 17850.