Least Common Multiple (LCM) of 175 and 138
The least common multiple (LCM) of 175 and 138 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 175 and 138?
First, calculate the GCD of 175 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 138 = 1 remainder 37 |
| 2 | 138 ÷ 37 = 3 remainder 27 |
| 3 | 37 ÷ 27 = 1 remainder 10 |
| 4 | 27 ÷ 10 = 2 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 65 | 1365 |
| 155 and 145 | 4495 |
| 105 and 103 | 10815 |
| 79 and 187 | 14773 |
| 109 and 197 | 21473 |