Least Common Multiple (LCM) of 138 and 96
The least common multiple (LCM) of 138 and 96 is 2208.
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 138 and 96?
First, calculate the GCD of 138 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 96 = 1 remainder 42 |
| 2 | 96 ÷ 42 = 2 remainder 12 |
| 3 | 42 ÷ 12 = 3 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 172 | 3440 |
| 126 and 111 | 4662 |
| 121 and 191 | 23111 |
| 73 and 155 | 11315 |
| 175 and 127 | 22225 |