Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 342 and 347 the smallest integer that is 118674 that is divisible by both numbers.
Least Common Multiple (LCM) of 342 and 347 is 118674.
LCM(342,347) = 118674
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 342 and 347. First we will calculate the prime factors of 342 and 347.
Prime Factorization of 342
2 | 342 |
3 | 171 |
3 | 57 |
19 | 19 |
1 |
Prime factors of 342 are 2, 3,19. Prime factorization of 342 in exponential form is:
342 = 21×32×191
Prime Factorization of 347
347 | 347 |
1 |
Prime factors of 347 are 347. Prime factorization of 347 in exponential form is:
347 = 3471
Now multiplying the highest exponent prime factors to calculate the LCM of 342 and 347.
LCM(342,347) = 21×32×191×3471
LCM(342,347) = 118674
Factors of 342
List of positive integer factors of 342 that divides 342 without a remainder.
1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
Factors of 347
List of positive integer factors of 347 that divides 347 without a remainder.
1, 347
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 342 and 347, than apply into the LCM equation.
GCF(342,347) = 1
LCM(342,347) = ( 342 × 347) / 1
LCM(342,347) = 118674 / 1
LCM(342,347) = 118674
(i) The LCM of 347 and 342 is associative
LCM of 342 and 347 = LCM of 347 and 342
1. What is the LCM of 342 and 347?
Answer: LCM of 342 and 347 is 118674.
2. What are the Factors of 342?
Answer: Factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342. There are 12 integers that are factors of 342. The greatest factor of 342 is 342.
3. What are the Factors of 347?
Answer: Factors of 347 are 1, 347. There are 2 integers that are factors of 347. The greatest factor of 347 is 347.
4. How to Find the LCM of 342 and 347?
Answer:
Least Common Multiple of 342 and 347 = 118674
Step 1: Find the prime factorization of 342
342 = 2 x 3 x 3 x 19
Step 2: Find the prime factorization of 347
347 = 347
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 118674 = 2 x 3 x 3 x 19 x 347
Step 4: Therefore, the least common multiple of 342 and 347 is 118674.