Least Common Multiple (LCM) of 101 and 168
The least common multiple (LCM) of 101 and 168 is 16968.
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 101 and 168?
First, calculate the GCD of 101 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 168 = 0 remainder 101 |
| 2 | 168 ÷ 101 = 1 remainder 67 |
| 3 | 101 ÷ 67 = 1 remainder 34 |
| 4 | 67 ÷ 34 = 1 remainder 33 |
| 5 | 34 ÷ 33 = 1 remainder 1 |
| 6 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 16 | 176 |
| 166 and 36 | 2988 |
| 185 and 56 | 10360 |
| 77 and 77 | 77 |
| 170 and 62 | 5270 |