Least Common Multiple (LCM) of 113 and 187
The least common multiple (LCM) of 113 and 187 is 21131.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 113 and 187?
First, calculate the GCD of 113 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 187 = 0 remainder 113 |
| 2 | 187 ÷ 113 = 1 remainder 74 |
| 3 | 113 ÷ 74 = 1 remainder 39 |
| 4 | 74 ÷ 39 = 1 remainder 35 |
| 5 | 39 ÷ 35 = 1 remainder 4 |
| 6 | 35 ÷ 4 = 8 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 105 | 8610 |
| 58 and 87 | 174 |
| 148 and 109 | 16132 |
| 102 and 49 | 4998 |
| 168 and 10 | 840 |