Least Common Multiple (LCM) of 142 and 174
The least common multiple (LCM) of 142 and 174 is 12354.
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 142 and 174?
First, calculate the GCD of 142 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 174 = 0 remainder 142 |
| 2 | 174 ÷ 142 = 1 remainder 32 |
| 3 | 142 ÷ 32 = 4 remainder 14 |
| 4 | 32 ÷ 14 = 2 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 106 | 20670 |
| 13 and 94 | 1222 |
| 89 and 189 | 16821 |
| 53 and 15 | 795 |
| 174 and 46 | 4002 |