Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 17234 and 17242 the smallest integer that is 148574314 that is divisible by both numbers.
Least Common Multiple (LCM) of 17234 and 17242 is 148574314.
LCM(17234,17242) = 148574314
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 17234 and 17242. First we will calculate the prime factors of 17234 and 17242.
Prime Factorization of 17234
2 | 17234 |
7 | 8617 |
1231 | 1231 |
1 |
Prime factors of 17234 are 2, 7,1231. Prime factorization of 17234 in exponential form is:
17234 = 21×71×12311
Prime Factorization of 17242
2 | 17242 |
37 | 8621 |
233 | 233 |
1 |
Prime factors of 17242 are 2, 37,233. Prime factorization of 17242 in exponential form is:
17242 = 21×371×2331
Now multiplying the highest exponent prime factors to calculate the LCM of 17234 and 17242.
LCM(17234,17242) = 21×71×371×2331×12311
LCM(17234,17242) = 148574314
Factors of 17234
List of positive integer factors of 17234 that divides 17234 without a remainder.
1, 2, 7, 14, 1231, 2462, 8617, 17234
Factors of 17242
List of positive integer factors of 17242 that divides 17242 without a remainder.
1, 2, 37, 74, 233, 466, 8621, 17242
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17234 and 17242, than apply into the LCM equation.
GCF(17234,17242) = 2
LCM(17234,17242) = ( 17234 × 17242) / 2
LCM(17234,17242) = 297148628 / 2
LCM(17234,17242) = 148574314
(i) The LCM of 17242 and 17234 is associative
LCM of 17234 and 17242 = LCM of 17242 and 17234
1. What is the LCM of 17234 and 17242?
Answer: LCM of 17234 and 17242 is 148574314.
2. What are the Factors of 17234?
Answer: Factors of 17234 are 1, 2, 7, 14, 1231, 2462, 8617, 17234. There are 8 integers that are factors of 17234. The greatest factor of 17234 is 17234.
3. What are the Factors of 17242?
Answer: Factors of 17242 are 1, 2, 37, 74, 233, 466, 8621, 17242. There are 8 integers that are factors of 17242. The greatest factor of 17242 is 17242.
4. How to Find the LCM of 17234 and 17242?
Answer:
Least Common Multiple of 17234 and 17242 = 148574314
Step 1: Find the prime factorization of 17234
17234 = 2 x 7 x 1231
Step 2: Find the prime factorization of 17242
17242 = 2 x 37 x 233
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 148574314 = 2 x 7 x 37 x 233 x 1231
Step 4: Therefore, the least common multiple of 17234 and 17242 is 148574314.