Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 229 and 232 the smallest integer that is 53128 that is divisible by both numbers.
Least Common Multiple (LCM) of 229 and 232 is 53128.
LCM(229,232) = 53128
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 229 and 232. First we will calculate the prime factors of 229 and 232.
Prime Factorization of 229
229 | 229 |
1 |
Prime factors of 229 are 229. Prime factorization of 229 in exponential form is:
229 = 2291
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 229 and 232.
LCM(229,232) = 23×291×2291
LCM(229,232) = 53128
Factors of 229
List of positive integer factors of 229 that divides 229 without a remainder.
1, 229
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 229 and 232, than apply into the LCM equation.
GCF(229,232) = 1
LCM(229,232) = ( 229 × 232) / 1
LCM(229,232) = 53128 / 1
LCM(229,232) = 53128
(i) The LCM of 232 and 229 is associative
LCM of 229 and 232 = LCM of 232 and 229
1. What is the LCM of 229 and 232?
Answer: LCM of 229 and 232 is 53128.
2. What are the Factors of 229?
Answer: Factors of 229 are 1, 229. There are 2 integers that are factors of 229. The greatest factor of 229 is 229.
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 229 and 232?
Answer:
Least Common Multiple of 229 and 232 = 53128
Step 1: Find the prime factorization of 229
229 = 229
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 = 53128 = 2 x 2 x 2 x 29 x 229
Step 4: Therefore, the least common multiple of 229 and 232 is 53128.