Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 203 and 208 the smallest integer that is 42224 that is divisible by both numbers.
Least Common Multiple (LCM) of 203 and 208 is 42224.
LCM(203,208) = 42224
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 203 and 208. First we will calculate the prime factors of 203 and 208.
Prime Factorization of 203
7 | 203 |
29 | 29 |
1 |
Prime factors of 203 are 7,29. Prime factorization of 203 in exponential form is:
203 = 71×291
Prime Factorization of 208
2 | 208 |
2 | 104 |
2 | 52 |
2 | 26 |
13 | 13 |
1 |
Prime factors of 208 are 2,13. Prime factorization of 208 in exponential form is:
208 = 24×131
Now multiplying the highest exponent prime factors to calculate the LCM of 203 and 208.
LCM(203,208) = 24×71×131×291
LCM(203,208) = 42224
Factors of 203
List of positive integer factors of 203 that divides 203 without a remainder.
1, 7, 29, 203
Factors of 208
List of positive integer factors of 208 that divides 208 without a remainder.
1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 203 and 208, than apply into the LCM equation.
GCF(203,208) = 1
LCM(203,208) = ( 203 × 208) / 1
LCM(203,208) = 42224 / 1
LCM(203,208) = 42224
(i) The LCM of 208 and 203 is associative
LCM of 203 and 208 = LCM of 208 and 203
1. What is the LCM of 203 and 208?
Answer: LCM of 203 and 208 is 42224.
2. What are the Factors of 203?
Answer: Factors of 203 are 1, 7, 29, 203. There are 4 integers that are factors of 203. The greatest factor of 203 is 203.
3. What are the Factors of 208?
Answer: Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. There are 10 integers that are factors of 208. The greatest factor of 208 is 208.
4. How to Find the LCM of 203 and 208?
Answer:
Least Common Multiple of 203 and 208 = 42224
Step 1: Find the prime factorization of 203
203 = 7 x 29
Step 2: Find the prime factorization of 208
208 = 2 x 2 x 2 x 2 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 42224 = 2 x 2 x 2 x 2 x 7 x 13 x 29
Step 4: Therefore, the least common multiple of 203 and 208 is 42224.