Least Common Multiple (LCM) of 74 and 114
The least common multiple (LCM) of 74 and 114 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 74 and 114?
First, calculate the GCD of 74 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 114 = 0 remainder 74 |
| 2 | 114 ÷ 74 = 1 remainder 40 |
| 3 | 74 ÷ 40 = 1 remainder 34 |
| 4 | 40 ÷ 34 = 1 remainder 6 |
| 5 | 34 ÷ 6 = 5 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 185 | 14245 |
| 135 and 136 | 18360 |
| 108 and 184 | 4968 |
| 74 and 130 | 4810 |
| 109 and 75 | 8175 |