Least Common Multiple (LCM) of 126 and 74
The least common multiple (LCM) of 126 and 74 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 126 and 74?
First, calculate the GCD of 126 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 74 = 1 remainder 52 |
| 2 | 74 ÷ 52 = 1 remainder 22 |
| 3 | 52 ÷ 22 = 2 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 162 | 15714 |
| 153 and 102 | 306 |
| 30 and 178 | 2670 |
| 185 and 33 | 6105 |
| 122 and 143 | 17446 |