Least Common Multiple (LCM) of 35 and 114
The least common multiple (LCM) of 35 and 114 is 3990.
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 114?
First, calculate the GCD of 35 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 114 = 0 remainder 35 |
| 2 | 114 ÷ 35 = 3 remainder 9 |
| 3 | 35 ÷ 9 = 3 remainder 8 |
| 4 | 9 ÷ 8 = 1 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 72 | 4248 |
| 133 and 183 | 24339 |
| 39 and 35 | 1365 |
| 166 and 125 | 20750 |
| 121 and 144 | 17424 |