Least Common Multiple (LCM) of 101 and 176
The least common multiple (LCM) of 101 and 176 is 17776.
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 176?
First, calculate the GCD of 101 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 176 = 0 remainder 101 |
| 2 | 176 ÷ 101 = 1 remainder 75 |
| 3 | 101 ÷ 75 = 1 remainder 26 |
| 4 | 75 ÷ 26 = 2 remainder 23 |
| 5 | 26 ÷ 23 = 1 remainder 3 |
| 6 | 23 ÷ 3 = 7 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 108 | 5724 |
| 169 and 84 | 14196 |
| 36 and 150 | 900 |
| 178 and 62 | 5518 |
| 146 and 123 | 17958 |