Least Common Multiple (LCM) of 70 and 125
The least common multiple (LCM) of 70 and 125 is 1750.
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 70 and 125?
First, calculate the GCD of 70 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 125 = 0 remainder 70 |
| 2 | 125 ÷ 70 = 1 remainder 55 |
| 3 | 70 ÷ 55 = 1 remainder 15 |
| 4 | 55 ÷ 15 = 3 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 175 | 175 |
| 165 and 82 | 13530 |
| 15 and 52 | 780 |
| 185 and 171 | 31635 |
| 162 and 120 | 3240 |