Least Common Multiple (LCM) of 114 and 74
The least common multiple (LCM) of 114 and 74 is 4218.
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 74?
First, calculate the GCD of 114 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 74 = 1 remainder 40 |
| 2 | 74 ÷ 40 = 1 remainder 34 |
| 3 | 40 ÷ 34 = 1 remainder 6 |
| 4 | 34 ÷ 6 = 5 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 156 | 3900 |
| 105 and 98 | 1470 |
| 181 and 107 | 19367 |
| 135 and 186 | 8370 |
| 54 and 164 | 4428 |