Least Common Multiple (LCM) of 145 and 56
The least common multiple (LCM) of 145 and 56 is 8120.
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 56?
First, calculate the GCD of 145 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 56 = 2 remainder 33 |
| 2 | 56 ÷ 33 = 1 remainder 23 |
| 3 | 33 ÷ 23 = 1 remainder 10 |
| 4 | 23 ÷ 10 = 2 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 59 | 4071 |
| 147 and 70 | 1470 |
| 72 and 69 | 1656 |
| 123 and 63 | 2583 |
| 80 and 112 | 560 |