Least Common Multiple (LCM) of 59 and 100
The least common multiple (LCM) of 59 and 100 is 5900.
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 100?
First, calculate the GCD of 59 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 100 = 0 remainder 59 |
| 2 | 100 ÷ 59 = 1 remainder 41 |
| 3 | 59 ÷ 41 = 1 remainder 18 |
| 4 | 41 ÷ 18 = 2 remainder 5 |
| 5 | 18 ÷ 5 = 3 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 146 | 11242 |
| 73 and 80 | 5840 |
| 153 and 11 | 1683 |
| 128 and 145 | 18560 |
| 193 and 195 | 37635 |