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 |
|---|---|
| 126 and 48 | 1008 |
| 159 and 144 | 7632 |
| 107 and 66 | 7062 |
| 74 and 42 | 1554 |
| 35 and 78 | 2730 |