Least Common Multiple (LCM) of 25 and 140
The least common multiple (LCM) of 25 and 140 is 700.
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 25 and 140?
First, calculate the GCD of 25 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 140 = 0 remainder 25 |
| 2 | 140 ÷ 25 = 5 remainder 15 |
| 3 | 25 ÷ 15 = 1 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 96 | 2784 |
| 150 and 178 | 13350 |
| 155 and 117 | 18135 |
| 182 and 47 | 8554 |
| 123 and 72 | 2952 |