Least Common Multiple (LCM) of 114 and 70
The least common multiple (LCM) of 114 and 70 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 114 and 70?
First, calculate the GCD of 114 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 70 = 1 remainder 44 |
| 2 | 70 ÷ 44 = 1 remainder 26 |
| 3 | 44 ÷ 26 = 1 remainder 18 |
| 4 | 26 ÷ 18 = 1 remainder 8 |
| 5 | 18 ÷ 8 = 2 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 61 | 10065 |
| 91 and 103 | 9373 |
| 78 and 92 | 3588 |
| 11 and 90 | 990 |
| 196 and 21 | 588 |