Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 218 and 223 the smallest integer that is 48614 that is divisible by both numbers.
Least Common Multiple (LCM) of 218 and 223 is 48614.
LCM(218,223) = 48614
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 218 and 223. First we will calculate the prime factors of 218 and 223.
Prime Factorization of 218
2 | 218 |
109 | 109 |
1 |
Prime factors of 218 are 2,109. Prime factorization of 218 in exponential form is:
218 = 21×1091
Prime Factorization of 223
223 | 223 |
1 |
Prime factors of 223 are 223. Prime factorization of 223 in exponential form is:
223 = 2231
Now multiplying the highest exponent prime factors to calculate the LCM of 218 and 223.
LCM(218,223) = 21×1091×2231
LCM(218,223) = 48614
Factors of 218
List of positive integer factors of 218 that divides 218 without a remainder.
1, 2, 109, 218
Factors of 223
List of positive integer factors of 223 that divides 223 without a remainder.
1, 223
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 218 and 223, than apply into the LCM equation.
GCF(218,223) = 1
LCM(218,223) = ( 218 × 223) / 1
LCM(218,223) = 48614 / 1
LCM(218,223) = 48614
(i) The LCM of 223 and 218 is associative
LCM of 218 and 223 = LCM of 223 and 218
1. What is the LCM of 218 and 223?
Answer: LCM of 218 and 223 is 48614.
2. What are the Factors of 218?
Answer: Factors of 218 are 1, 2, 109, 218. There are 4 integers that are factors of 218. The greatest factor of 218 is 218.
3. What are the Factors of 223?
Answer: Factors of 223 are 1, 223. There are 2 integers that are factors of 223. The greatest factor of 223 is 223.
4. How to Find the LCM of 218 and 223?
Answer:
Least Common Multiple of 218 and 223 = 48614
Step 1: Find the prime factorization of 218
218 = 2 x 109
Step 2: Find the prime factorization of 223
223 = 223
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 48614 = 2 x 109 x 223
Step 4: Therefore, the least common multiple of 218 and 223 is 48614.