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 |
|---|---|
| 165 and 146 | 24090 |
| 182 and 38 | 3458 |
| 164 and 19 | 3116 |
| 181 and 111 | 20091 |
| 157 and 52 | 8164 |