Least Common Multiple (LCM) of 74 and 145
The least common multiple (LCM) of 74 and 145 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 74 and 145?
First, calculate the GCD of 74 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 145 = 0 remainder 74 |
| 2 | 145 ÷ 74 = 1 remainder 71 |
| 3 | 74 ÷ 71 = 1 remainder 3 |
| 4 | 71 ÷ 3 = 23 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 42 | 966 |
| 59 and 139 | 8201 |
| 156 and 163 | 25428 |
| 84 and 161 | 1932 |
| 145 and 196 | 28420 |