Least Common Multiple (LCM) of 56 and 35
The least common multiple (LCM) of 56 and 35 is 280.
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 35?
First, calculate the GCD of 56 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 35 = 1 remainder 21 |
| 2 | 35 ÷ 21 = 1 remainder 14 |
| 3 | 21 ÷ 14 = 1 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 26 | 3250 |
| 171 and 114 | 342 |
| 75 and 80 | 1200 |
| 65 and 114 | 7410 |
| 19 and 182 | 3458 |