Least Common Multiple (LCM) of 60 and 83
The least common multiple (LCM) of 60 and 83 is 4980.
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 60 and 83?
First, calculate the GCD of 60 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 83 = 0 remainder 60 |
| 2 | 83 ÷ 60 = 1 remainder 23 |
| 3 | 60 ÷ 23 = 2 remainder 14 |
| 4 | 23 ÷ 14 = 1 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 120 | 7080 |
| 83 and 143 | 11869 |
| 35 and 90 | 630 |
| 197 and 137 | 26989 |
| 149 and 94 | 14006 |