Least Common Multiple (LCM) of 138 and 175
The least common multiple (LCM) of 138 and 175 is 24150.
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 175?
First, calculate the GCD of 138 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 175 = 0 remainder 138 |
| 2 | 175 ÷ 138 = 1 remainder 37 |
| 3 | 138 ÷ 37 = 3 remainder 27 |
| 4 | 37 ÷ 27 = 1 remainder 10 |
| 5 | 27 ÷ 10 = 2 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 113 | 14690 |
| 22 and 106 | 1166 |
| 180 and 128 | 5760 |
| 70 and 42 | 210 |
| 192 and 102 | 3264 |