Least Common Multiple (LCM) of 174 and 64
The least common multiple (LCM) of 174 and 64 is 5568.
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 64?
First, calculate the GCD of 174 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 64 = 2 remainder 46 |
| 2 | 64 ÷ 46 = 1 remainder 18 |
| 3 | 46 ÷ 18 = 2 remainder 10 |
| 4 | 18 ÷ 10 = 1 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 162 | 10530 |
| 131 and 161 | 21091 |
| 125 and 90 | 2250 |
| 31 and 119 | 3689 |
| 106 and 74 | 3922 |