Least Common Multiple (LCM) of 138 and 174
The least common multiple (LCM) of 138 and 174 is 4002.
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 174?
First, calculate the GCD of 138 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 174 = 0 remainder 138 |
| 2 | 174 ÷ 138 = 1 remainder 36 |
| 3 | 138 ÷ 36 = 3 remainder 30 |
| 4 | 36 ÷ 30 = 1 remainder 6 |
| 5 | 30 ÷ 6 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 67 | 7102 |
| 16 and 111 | 1776 |
| 134 and 119 | 15946 |
| 185 and 39 | 7215 |
| 101 and 12 | 1212 |