Least Common Multiple (LCM) of 89 and 101
The least common multiple (LCM) of 89 and 101 is 8989.
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 89 and 101?
First, calculate the GCD of 89 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 101 = 0 remainder 89 |
| 2 | 101 ÷ 89 = 1 remainder 12 |
| 3 | 89 ÷ 12 = 7 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 135 | 5535 |
| 32 and 72 | 288 |
| 59 and 33 | 1947 |
| 20 and 102 | 1020 |
| 110 and 107 | 11770 |