Least Common Multiple (LCM) of 59 and 174
The least common multiple (LCM) of 59 and 174 is 10266.
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 59 and 174?
First, calculate the GCD of 59 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 174 = 0 remainder 59 |
| 2 | 174 ÷ 59 = 2 remainder 56 |
| 3 | 59 ÷ 56 = 1 remainder 3 |
| 4 | 56 ÷ 3 = 18 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 123 | 19434 |
| 165 and 113 | 18645 |
| 112 and 40 | 560 |
| 54 and 148 | 3996 |
| 142 and 120 | 8520 |