Least Common Multiple (LCM) of 120 and 145
The least common multiple (LCM) of 120 and 145 is 3480.
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 120 and 145?
First, calculate the GCD of 120 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 145 = 0 remainder 120 |
| 2 | 145 ÷ 120 = 1 remainder 25 |
| 3 | 120 ÷ 25 = 4 remainder 20 |
| 4 | 25 ÷ 20 = 1 remainder 5 |
| 5 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 50 | 3050 |
| 87 and 54 | 1566 |
| 80 and 124 | 2480 |
| 65 and 116 | 7540 |
| 17 and 91 | 1547 |