Least Common Multiple (LCM) of 174 and 142
The least common multiple (LCM) of 174 and 142 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 174 and 142?
First, calculate the GCD of 174 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 142 = 1 remainder 32 |
| 2 | 142 ÷ 32 = 4 remainder 14 |
| 3 | 32 ÷ 14 = 2 remainder 4 |
| 4 | 14 ÷ 4 = 3 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 123 | 4305 |
| 138 and 191 | 26358 |
| 104 and 99 | 10296 |
| 14 and 111 | 1554 |
| 112 and 30 | 1680 |