Least Common Multiple (LCM) of 34 and 174
The least common multiple (LCM) of 34 and 174 is 2958.
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 34 and 174?
First, calculate the GCD of 34 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 174 = 0 remainder 34 |
| 2 | 174 ÷ 34 = 5 remainder 4 |
| 3 | 34 ÷ 4 = 8 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 110 | 1760 |
| 78 and 199 | 15522 |
| 115 and 153 | 17595 |
| 58 and 51 | 2958 |
| 174 and 127 | 22098 |