Least Common Multiple (LCM) of 48 and 137
The least common multiple (LCM) of 48 and 137 is 6576.
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 137?
First, calculate the GCD of 48 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 137 = 0 remainder 48 |
| 2 | 137 ÷ 48 = 2 remainder 41 |
| 3 | 48 ÷ 41 = 1 remainder 7 |
| 4 | 41 ÷ 7 = 5 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 119 | 1785 |
| 51 and 125 | 6375 |
| 137 and 121 | 16577 |
| 104 and 47 | 4888 |
| 137 and 173 | 23701 |