Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 226 and 232 the smallest integer that is 26216 that is divisible by both numbers.
Least Common Multiple (LCM) of 226 and 232 is 26216.
LCM(226,232) = 26216
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 226 and 232. First we will calculate the prime factors of 226 and 232.
Prime Factorization of 226
2 | 226 |
113 | 113 |
1 |
Prime factors of 226 are 2,113. Prime factorization of 226 in exponential form is:
226 = 21×1131
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 226 and 232.
LCM(226,232) = 23×291×1131
LCM(226,232) = 26216
Factors of 226
List of positive integer factors of 226 that divides 226 without a remainder.
1, 2, 113, 226
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 226 and 232, than apply into the LCM equation.
GCF(226,232) = 2
LCM(226,232) = ( 226 × 232) / 2
LCM(226,232) = 52432 / 2
LCM(226,232) = 26216
(i) The LCM of 232 and 226 is associative
LCM of 226 and 232 = LCM of 232 and 226
1. What is the LCM of 226 and 232?
Answer: LCM of 226 and 232 is 26216.
2. What are the Factors of 226?
Answer: Factors of 226 are 1, 2, 113, 226. There are 4 integers that are factors of 226. The greatest factor of 226 is 226.
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 226 and 232?
Answer:
Least Common Multiple of 226 and 232 = 26216
Step 1: Find the prime factorization of 226
226 = 2 x 113
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 = 26216 = 2 x 2 x 2 x 29 x 113
Step 4: Therefore, the least common multiple of 226 and 232 is 26216.