Least Common Multiple (LCM) of 35 and 56
The least common multiple (LCM) of 35 and 56 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 35 and 56?
First, calculate the GCD of 35 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 56 = 0 remainder 35 |
| 2 | 56 ÷ 35 = 1 remainder 21 |
| 3 | 35 ÷ 21 = 1 remainder 14 |
| 4 | 21 ÷ 14 = 1 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 128 | 4224 |
| 24 and 159 | 1272 |
| 183 and 67 | 12261 |
| 51 and 148 | 7548 |
| 153 and 106 | 16218 |