Least Common Multiple (LCM) of 138 and 16
The least common multiple (LCM) of 138 and 16 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 138 and 16?
First, calculate the GCD of 138 and 16 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 16 = 8 remainder 10 |
| 2 | 16 ÷ 10 = 1 remainder 6 |
| 3 | 10 ÷ 6 = 1 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 87 | 3567 |
| 108 and 173 | 18684 |
| 152 and 169 | 25688 |
| 184 and 167 | 30728 |
| 19 and 144 | 2736 |