Least Common Multiple (LCM) of 145 and 168
The least common multiple (LCM) of 145 and 168 is 24360.
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 168?
First, calculate the GCD of 145 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 168 = 0 remainder 145 |
| 2 | 168 ÷ 145 = 1 remainder 23 |
| 3 | 145 ÷ 23 = 6 remainder 7 |
| 4 | 23 ÷ 7 = 3 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 20 | 1540 |
| 134 and 173 | 23182 |
| 10 and 90 | 90 |
| 169 and 136 | 22984 |
| 111 and 147 | 5439 |