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 229 the smallest integer that is 51754 that is divisible by both numbers.
Least Common Multiple (LCM) of 226 and 229 is 51754.
LCM(226,229) = 51754
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 229. First we will calculate the prime factors of 226 and 229.
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 229
229 | 229 |
1 |
Prime factors of 229 are 229. Prime factorization of 229 in exponential form is:
229 = 2291
Now multiplying the highest exponent prime factors to calculate the LCM of 226 and 229.
LCM(226,229) = 21×1131×2291
LCM(226,229) = 51754
Factors of 226
List of positive integer factors of 226 that divides 226 without a remainder.
1, 2, 113, 226
Factors of 229
List of positive integer factors of 229 that divides 229 without a remainder.
1, 229
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 226 and 229, than apply into the LCM equation.
GCF(226,229) = 1
LCM(226,229) = ( 226 × 229) / 1
LCM(226,229) = 51754 / 1
LCM(226,229) = 51754
(i) The LCM of 229 and 226 is associative
LCM of 226 and 229 = LCM of 229 and 226
1. What is the LCM of 226 and 229?
Answer: LCM of 226 and 229 is 51754.
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 229?
Answer: Factors of 229 are 1, 229. There are 2 integers that are factors of 229. The greatest factor of 229 is 229.
4. How to Find the LCM of 226 and 229?
Answer:
Least Common Multiple of 226 and 229 = 51754
Step 1: Find the prime factorization of 226
226 = 2 x 113
Step 2: Find the prime factorization of 229
229 = 229
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 51754 = 2 x 113 x 229
Step 4: Therefore, the least common multiple of 226 and 229 is 51754.