Least Common Multiple (LCM) of 100 and 59
The least common multiple (LCM) of 100 and 59 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 100 and 59?
First, calculate the GCD of 100 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 59 = 1 remainder 41 |
| 2 | 59 ÷ 41 = 1 remainder 18 |
| 3 | 41 ÷ 18 = 2 remainder 5 |
| 4 | 18 ÷ 5 = 3 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 174 | 3828 |
| 137 and 157 | 21509 |
| 106 and 30 | 1590 |
| 148 and 171 | 25308 |
| 96 and 102 | 1632 |