Least Common Multiple (LCM) of 145 and 74
The least common multiple (LCM) of 145 and 74 is 10730.
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 145 and 74?
First, calculate the GCD of 145 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 74 = 1 remainder 71 |
| 2 | 74 ÷ 71 = 1 remainder 3 |
| 3 | 71 ÷ 3 = 23 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 36 | 2124 |
| 176 and 166 | 14608 |
| 73 and 197 | 14381 |
| 92 and 172 | 3956 |
| 153 and 138 | 7038 |