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 17235 the smallest integer that is 296924580 that is divisible by both numbers.
Least Common Multiple (LCM) of 17228 and 17235 is 296924580.
LCM(17228,17235) = 296924580
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 17235. First we will calculate the prime factors of 17228 and 17235.
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 17235
3 | 17235 |
3 | 5745 |
5 | 1915 |
383 | 383 |
1 |
Prime factors of 17235 are 3, 5,383. Prime factorization of 17235 in exponential form is:
17235 = 32×51×3831
Now multiplying the highest exponent prime factors to calculate the LCM of 17228 and 17235.
LCM(17228,17235) = 22×32×51×591×731×3831
LCM(17228,17235) = 296924580
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 17235
List of positive integer factors of 17235 that divides 17235 without a remainder.
1, 3, 5, 9, 15, 45, 383, 1149, 1915, 3447, 5745, 17235
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17228 and 17235, than apply into the LCM equation.
GCF(17228,17235) = 1
LCM(17228,17235) = ( 17228 × 17235) / 1
LCM(17228,17235) = 296924580 / 1
LCM(17228,17235) = 296924580
(i) The LCM of 17235 and 17228 is associative
LCM of 17228 and 17235 = LCM of 17235 and 17228
1. What is the LCM of 17228 and 17235?
Answer: LCM of 17228 and 17235 is 296924580.
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 17235?
Answer: Factors of 17235 are 1, 3, 5, 9, 15, 45, 383, 1149, 1915, 3447, 5745, 17235. There are 12 integers that are factors of 17235. The greatest factor of 17235 is 17235.
4. How to Find the LCM of 17228 and 17235?
Answer:
Least Common Multiple of 17228 and 17235 = 296924580
Step 1: Find the prime factorization of 17228
17228 = 2 x 2 x 59 x 73
Step 2: Find the prime factorization of 17235
17235 = 3 x 3 x 5 x 383
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 296924580 = 2 x 2 x 3 x 3 x 5 x 59 x 73 x 383
Step 4: Therefore, the least common multiple of 17228 and 17235 is 296924580.