Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 343 and 346 the smallest integer that is 118678 that is divisible by both numbers.
Least Common Multiple (LCM) of 343 and 346 is 118678.
LCM(343,346) = 118678
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 343 and 346. First we will calculate the prime factors of 343 and 346.
Prime Factorization of 343
7 | 343 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 343 are 7. Prime factorization of 343 in exponential form is:
343 = 73
Prime Factorization of 346
2 | 346 |
173 | 173 |
1 |
Prime factors of 346 are 2,173. Prime factorization of 346 in exponential form is:
346 = 21×1731
Now multiplying the highest exponent prime factors to calculate the LCM of 343 and 346.
LCM(343,346) = 21×73×1731
LCM(343,346) = 118678
Factors of 343
List of positive integer factors of 343 that divides 343 without a remainder.
1, 7, 49, 343
Factors of 346
List of positive integer factors of 346 that divides 346 without a remainder.
1, 2, 173, 346
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 343 and 346, than apply into the LCM equation.
GCF(343,346) = 1
LCM(343,346) = ( 343 × 346) / 1
LCM(343,346) = 118678 / 1
LCM(343,346) = 118678
(i) The LCM of 346 and 343 is associative
LCM of 343 and 346 = LCM of 346 and 343
1. What is the LCM of 343 and 346?
Answer: LCM of 343 and 346 is 118678.
2. What are the Factors of 343?
Answer: Factors of 343 are 1, 7, 49, 343. There are 4 integers that are factors of 343. The greatest factor of 343 is 343.
3. What are the Factors of 346?
Answer: Factors of 346 are 1, 2, 173, 346. There are 4 integers that are factors of 346. The greatest factor of 346 is 346.
4. How to Find the LCM of 343 and 346?
Answer:
Least Common Multiple of 343 and 346 = 118678
Step 1: Find the prime factorization of 343
343 = 7 x 7 x 7
Step 2: Find the prime factorization of 346
346 = 2 x 173
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 118678 = 2 x 7 x 7 x 7 x 173
Step 4: Therefore, the least common multiple of 343 and 346 is 118678.