Least Common Multiple (LCM) of 137 and 48
The least common multiple (LCM) of 137 and 48 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 137 and 48?
First, calculate the GCD of 137 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 48 = 2 remainder 41 |
| 2 | 48 ÷ 41 = 1 remainder 7 |
| 3 | 41 ÷ 7 = 5 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 117 | 3978 |
| 185 and 178 | 32930 |
| 62 and 82 | 2542 |
| 137 and 168 | 23016 |
| 143 and 167 | 23881 |