Least Common Multiple (LCM) of 59 and 84
The least common multiple (LCM) of 59 and 84 is 4956.
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 59 and 84?
First, calculate the GCD of 59 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 84 = 0 remainder 59 |
| 2 | 84 ÷ 59 = 1 remainder 25 |
| 3 | 59 ÷ 25 = 2 remainder 9 |
| 4 | 25 ÷ 9 = 2 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 176 | 18480 |
| 134 and 49 | 6566 |
| 54 and 119 | 6426 |
| 184 and 136 | 3128 |
| 48 and 42 | 336 |