Least Common Multiple (LCM) of 145 and 67
The least common multiple (LCM) of 145 and 67 is 9715.
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 67?
First, calculate the GCD of 145 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 67 = 2 remainder 11 |
| 2 | 67 ÷ 11 = 6 remainder 1 |
| 3 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 35 | 805 |
| 10 and 62 | 310 |
| 21 and 77 | 231 |
| 63 and 13 | 819 |
| 169 and 165 | 27885 |