Least Common Multiple (LCM) of 47 and 120
The least common multiple (LCM) of 47 and 120 is 5640.
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 47 and 120?
First, calculate the GCD of 47 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 120 = 0 remainder 47 |
| 2 | 120 ÷ 47 = 2 remainder 26 |
| 3 | 47 ÷ 26 = 1 remainder 21 |
| 4 | 26 ÷ 21 = 1 remainder 5 |
| 5 | 21 ÷ 5 = 4 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 62 | 5704 |
| 25 and 42 | 1050 |
| 123 and 151 | 18573 |
| 145 and 102 | 14790 |
| 110 and 30 | 330 |