Least Common Multiple (LCM) of 35 and 118
The least common multiple (LCM) of 35 and 118 is 4130.
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 118?
First, calculate the GCD of 35 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 118 = 0 remainder 35 |
| 2 | 118 ÷ 35 = 3 remainder 13 |
| 3 | 35 ÷ 13 = 2 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 72 | 6840 |
| 117 and 114 | 4446 |
| 135 and 88 | 11880 |
| 112 and 94 | 5264 |
| 158 and 164 | 12956 |