Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 348 and 349 the smallest integer that is 121452 that is divisible by both numbers.
Least Common Multiple (LCM) of 348 and 349 is 121452.
LCM(348,349) = 121452
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 348 and 349. First we will calculate the prime factors of 348 and 349.
Prime Factorization of 348
2 | 348 |
2 | 174 |
3 | 87 |
29 | 29 |
1 |
Prime factors of 348 are 2, 3,29. Prime factorization of 348 in exponential form is:
348 = 22×31×291
Prime Factorization of 349
349 | 349 |
1 |
Prime factors of 349 are 349. Prime factorization of 349 in exponential form is:
349 = 3491
Now multiplying the highest exponent prime factors to calculate the LCM of 348 and 349.
LCM(348,349) = 22×31×291×3491
LCM(348,349) = 121452
Factors of 348
List of positive integer factors of 348 that divides 348 without a remainder.
1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348
Factors of 349
List of positive integer factors of 349 that divides 349 without a remainder.
1, 349
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 348 and 349, than apply into the LCM equation.
GCF(348,349) = 1
LCM(348,349) = ( 348 × 349) / 1
LCM(348,349) = 121452 / 1
LCM(348,349) = 121452
(i) The LCM of 349 and 348 is associative
LCM of 348 and 349 = LCM of 349 and 348
1. What is the LCM of 348 and 349?
Answer: LCM of 348 and 349 is 121452.
2. What are the Factors of 348?
Answer: Factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348. There are 12 integers that are factors of 348. The greatest factor of 348 is 348.
3. What are the Factors of 349?
Answer: Factors of 349 are 1, 349. There are 2 integers that are factors of 349. The greatest factor of 349 is 349.
4. How to Find the LCM of 348 and 349?
Answer:
Least Common Multiple of 348 and 349 = 121452
Step 1: Find the prime factorization of 348
348 = 2 x 2 x 3 x 29
Step 2: Find the prime factorization of 349
349 = 349
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 121452 = 2 x 2 x 3 x 29 x 349
Step 4: Therefore, the least common multiple of 348 and 349 is 121452.