Least Common Multiple (LCM) of 56 and 125
The least common multiple (LCM) of 56 and 125 is 7000.
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 56 and 125?
First, calculate the GCD of 56 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 125 = 0 remainder 56 |
| 2 | 125 ÷ 56 = 2 remainder 13 |
| 3 | 56 ÷ 13 = 4 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 47 | 6768 |
| 87 and 105 | 3045 |
| 32 and 131 | 4192 |
| 106 and 109 | 11554 |
| 113 and 162 | 18306 |