Least Common Multiple (LCM) of 74 and 126
The least common multiple (LCM) of 74 and 126 is 4662.
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 126?
First, calculate the GCD of 74 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 126 = 0 remainder 74 |
| 2 | 126 ÷ 74 = 1 remainder 52 |
| 3 | 74 ÷ 52 = 1 remainder 22 |
| 4 | 52 ÷ 22 = 2 remainder 8 |
| 5 | 22 ÷ 8 = 2 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 62 | 4650 |
| 38 and 182 | 3458 |
| 46 and 25 | 1150 |
| 154 and 61 | 9394 |
| 18 and 184 | 1656 |