Least Common Multiple (LCM) of 175 and 38
The least common multiple (LCM) of 175 and 38 is 6650.
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 38?
First, calculate the GCD of 175 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 38 = 4 remainder 23 |
| 2 | 38 ÷ 23 = 1 remainder 15 |
| 3 | 23 ÷ 15 = 1 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 112 | 560 |
| 50 and 33 | 1650 |
| 111 and 138 | 5106 |
| 144 and 167 | 24048 |
| 170 and 70 | 1190 |