Least Common Multiple (LCM) of 117 and 35
The least common multiple (LCM) of 117 and 35 is 4095.
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 117 and 35?
First, calculate the GCD of 117 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 35 = 3 remainder 12 |
| 2 | 35 ÷ 12 = 2 remainder 11 |
| 3 | 12 ÷ 11 = 1 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 120 | 360 |
| 116 and 151 | 17516 |
| 101 and 138 | 13938 |
| 169 and 36 | 6084 |
| 125 and 105 | 2625 |