Least Common Multiple (LCM) of 74 and 125
The least common multiple (LCM) of 74 and 125 is 9250.
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 74 and 125?
First, calculate the GCD of 74 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 125 = 0 remainder 74 |
| 2 | 125 ÷ 74 = 1 remainder 51 |
| 3 | 74 ÷ 51 = 1 remainder 23 |
| 4 | 51 ÷ 23 = 2 remainder 5 |
| 5 | 23 ÷ 5 = 4 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 68 | 3332 |
| 40 and 168 | 840 |
| 69 and 29 | 2001 |
| 200 and 120 | 600 |
| 17 and 122 | 2074 |