Least Common Multiple (LCM) of 35 and 57
The least common multiple (LCM) of 35 and 57 is 1995.
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 57?
First, calculate the GCD of 35 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 57 = 0 remainder 35 |
| 2 | 57 ÷ 35 = 1 remainder 22 |
| 3 | 35 ÷ 22 = 1 remainder 13 |
| 4 | 22 ÷ 13 = 1 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 78 | 13650 |
| 60 and 55 | 660 |
| 44 and 106 | 2332 |
| 177 and 17 | 3009 |
| 140 and 95 | 2660 |