Least Common Multiple (LCM) of 174 and 113
The least common multiple (LCM) of 174 and 113 is 19662.
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 113?
First, calculate the GCD of 174 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 113 = 1 remainder 61 |
| 2 | 113 ÷ 61 = 1 remainder 52 |
| 3 | 61 ÷ 52 = 1 remainder 9 |
| 4 | 52 ÷ 9 = 5 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 158 | 10744 |
| 61 and 54 | 3294 |
| 89 and 137 | 12193 |
| 102 and 114 | 1938 |
| 66 and 133 | 8778 |