Least Common Multiple (LCM) of 48 and 138
The least common multiple (LCM) of 48 and 138 is 1104.
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 138?
First, calculate the GCD of 48 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 138 = 0 remainder 48 |
| 2 | 138 ÷ 48 = 2 remainder 42 |
| 3 | 48 ÷ 42 = 1 remainder 6 |
| 4 | 42 ÷ 6 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 101 | 10302 |
| 68 and 184 | 3128 |
| 40 and 155 | 1240 |
| 59 and 187 | 11033 |
| 92 and 14 | 644 |