Least Common Multiple (LCM) of 145 and 101
The least common multiple (LCM) of 145 and 101 is 14645.
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 145 and 101?
First, calculate the GCD of 145 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 101 = 1 remainder 44 |
| 2 | 101 ÷ 44 = 2 remainder 13 |
| 3 | 44 ÷ 13 = 3 remainder 5 |
| 4 | 13 ÷ 5 = 2 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 |
|---|---|
| 85 and 101 | 8585 |
| 177 and 35 | 6195 |
| 167 and 77 | 12859 |
| 134 and 47 | 6298 |
| 130 and 103 | 13390 |