Least Common Multiple (LCM) of 48 and 113
The least common multiple (LCM) of 48 and 113 is 5424.
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 48 and 113?
First, calculate the GCD of 48 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 113 = 0 remainder 48 |
| 2 | 113 ÷ 48 = 2 remainder 17 |
| 3 | 48 ÷ 17 = 2 remainder 14 |
| 4 | 17 ÷ 14 = 1 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 160 | 5920 |
| 36 and 129 | 1548 |
| 103 and 119 | 12257 |
| 133 and 15 | 1995 |
| 175 and 173 | 30275 |