Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 17230 and 17234 the smallest integer that is 148470910 that is divisible by both numbers.
Least Common Multiple (LCM) of 17230 and 17234 is 148470910.
LCM(17230,17234) = 148470910
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 17230 and 17234. First we will calculate the prime factors of 17230 and 17234.
Prime Factorization of 17230
2 | 17230 |
5 | 8615 |
1723 | 1723 |
1 |
Prime factors of 17230 are 2, 5,1723. Prime factorization of 17230 in exponential form is:
17230 = 21×51×17231
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 17230 and 17234.
LCM(17230,17234) = 21×51×71×12311×17231
LCM(17230,17234) = 148470910
Factors of 17230
List of positive integer factors of 17230 that divides 17230 without a remainder.
1, 2, 5, 10, 1723, 3446, 8615, 17230
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 17230 and 17234, than apply into the LCM equation.
GCF(17230,17234) = 2
LCM(17230,17234) = ( 17230 × 17234) / 2
LCM(17230,17234) = 296941820 / 2
LCM(17230,17234) = 148470910
(i) The LCM of 17234 and 17230 is associative
LCM of 17230 and 17234 = LCM of 17234 and 17230
1. What is the LCM of 17230 and 17234?
Answer: LCM of 17230 and 17234 is 148470910.
2. What are the Factors of 17230?
Answer: Factors of 17230 are 1, 2, 5, 10, 1723, 3446, 8615, 17230. There are 8 integers that are factors of 17230. The greatest factor of 17230 is 17230.
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 17230 and 17234?
Answer:
Least Common Multiple of 17230 and 17234 = 148470910
Step 1: Find the prime factorization of 17230
17230 = 2 x 5 x 1723
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 = 148470910 = 2 x 5 x 7 x 1231 x 1723
Step 4: Therefore, the least common multiple of 17230 and 17234 is 148470910.