Least Common Multiple (LCM) of 74 and 142
The least common multiple (LCM) of 74 and 142 is 5254.
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 142?
First, calculate the GCD of 74 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 142 = 0 remainder 74 |
| 2 | 142 ÷ 74 = 1 remainder 68 |
| 3 | 74 ÷ 68 = 1 remainder 6 |
| 4 | 68 ÷ 6 = 11 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 33 | 1980 |
| 106 and 116 | 6148 |
| 167 and 68 | 11356 |
| 112 and 38 | 2128 |
| 130 and 149 | 19370 |