Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 230 and 232 the smallest integer that is 26680 that is divisible by both numbers.
Least Common Multiple (LCM) of 230 and 232 is 26680.
LCM(230,232) = 26680
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 230 and 232. First we will calculate the prime factors of 230 and 232.
Prime Factorization of 230
2 | 230 |
5 | 115 |
23 | 23 |
1 |
Prime factors of 230 are 2, 5,23. Prime factorization of 230 in exponential form is:
230 = 21×51×231
Prime Factorization of 232
2 | 232 |
2 | 116 |
2 | 58 |
29 | 29 |
1 |
Prime factors of 232 are 2,29. Prime factorization of 232 in exponential form is:
232 = 23×291
Now multiplying the highest exponent prime factors to calculate the LCM of 230 and 232.
LCM(230,232) = 23×51×231×291
LCM(230,232) = 26680
Factors of 230
List of positive integer factors of 230 that divides 230 without a remainder.
1, 2, 5, 10, 23, 46, 115, 230
Factors of 232
List of positive integer factors of 232 that divides 232 without a remainder.
1, 2, 4, 8, 29, 58, 116, 232
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 230 and 232, than apply into the LCM equation.
GCF(230,232) = 2
LCM(230,232) = ( 230 × 232) / 2
LCM(230,232) = 53360 / 2
LCM(230,232) = 26680
(i) The LCM of 232 and 230 is associative
LCM of 230 and 232 = LCM of 232 and 230
1. What is the LCM of 230 and 232?
Answer: LCM of 230 and 232 is 26680.
2. What are the Factors of 230?
Answer: Factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230. There are 8 integers that are factors of 230. The greatest factor of 230 is 230.
3. What are the Factors of 232?
Answer: Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232. There are 8 integers that are factors of 232. The greatest factor of 232 is 232.
4. How to Find the LCM of 230 and 232?
Answer:
Least Common Multiple of 230 and 232 = 26680
Step 1: Find the prime factorization of 230
230 = 2 x 5 x 23
Step 2: Find the prime factorization of 232
232 = 2 x 2 x 2 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 26680 = 2 x 2 x 2 x 5 x 23 x 29
Step 4: Therefore, the least common multiple of 230 and 232 is 26680.