Least Common Multiple (LCM) of 64 and 174
The least common multiple (LCM) of 64 and 174 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 64 and 174?
First, calculate the GCD of 64 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 174 = 0 remainder 64 |
| 2 | 174 ÷ 64 = 2 remainder 46 |
| 3 | 64 ÷ 46 = 1 remainder 18 |
| 4 | 46 ÷ 18 = 2 remainder 10 |
| 5 | 18 ÷ 10 = 1 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 37 | 5550 |
| 43 and 12 | 516 |
| 135 and 161 | 21735 |
| 70 and 158 | 5530 |
| 60 and 14 | 420 |