Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 17228 and 17234 the smallest integer that is 148453676 that is divisible by both numbers.
Least Common Multiple (LCM) of 17228 and 17234 is 148453676.
LCM(17228,17234) = 148453676
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 17228 and 17234. First we will calculate the prime factors of 17228 and 17234.
Prime Factorization of 17228
2 | 17228 |
2 | 8614 |
59 | 4307 |
73 | 73 |
1 |
Prime factors of 17228 are 2, 59,73. Prime factorization of 17228 in exponential form is:
17228 = 22×591×731
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
Now multiplying the highest exponent prime factors to calculate the LCM of 17228 and 17234.
LCM(17228,17234) = 22×71×591×731×12311
LCM(17228,17234) = 148453676
Factors of 17228
List of positive integer factors of 17228 that divides 17228 without a remainder.
1, 2, 4, 59, 73, 118, 146, 236, 292, 4307, 8614, 17228
Factors of 17234
List of positive integer factors of 17234 that divides 17234 without a remainder.
1, 2, 7, 14, 1231, 2462, 8617, 17234
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17228 and 17234, than apply into the LCM equation.
GCF(17228,17234) = 2
LCM(17228,17234) = ( 17228 × 17234) / 2
LCM(17228,17234) = 296907352 / 2
LCM(17228,17234) = 148453676
(i) The LCM of 17234 and 17228 is associative
LCM of 17228 and 17234 = LCM of 17234 and 17228
1. What is the LCM of 17228 and 17234?
Answer: LCM of 17228 and 17234 is 148453676.
2. What are the Factors of 17228?
Answer: Factors of 17228 are 1, 2, 4, 59, 73, 118, 146, 236, 292, 4307, 8614, 17228. There are 12 integers that are factors of 17228. The greatest factor of 17228 is 17228.
3. 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.
4. How to Find the LCM of 17228 and 17234?
Answer:
Least Common Multiple of 17228 and 17234 = 148453676
Step 1: Find the prime factorization of 17228
17228 = 2 x 2 x 59 x 73
Step 2: Find the prime factorization of 17234
17234 = 2 x 7 x 1231
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 148453676 = 2 x 2 x 7 x 59 x 73 x 1231
Step 4: Therefore, the least common multiple of 17228 and 17234 is 148453676.