Least Common Multiple (LCM) of 113 and 148
The least common multiple (LCM) of 113 and 148 is 16724.
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 148?
First, calculate the GCD of 113 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 148 = 0 remainder 113 |
| 2 | 148 ÷ 113 = 1 remainder 35 |
| 3 | 113 ÷ 35 = 3 remainder 8 |
| 4 | 35 ÷ 8 = 4 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 49 | 1519 |
| 171 and 72 | 1368 |
| 166 and 82 | 6806 |
| 74 and 127 | 9398 |
| 20 and 137 | 2740 |