Least Common Multiple (LCM) of 72 and 101
The least common multiple (LCM) of 72 and 101 is 7272.
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 72 and 101?
First, calculate the GCD of 72 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 101 = 0 remainder 72 |
| 2 | 101 ÷ 72 = 1 remainder 29 |
| 3 | 72 ÷ 29 = 2 remainder 14 |
| 4 | 29 ÷ 14 = 2 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 144 | 27792 |
| 122 and 42 | 2562 |
| 169 and 45 | 7605 |
| 120 and 76 | 2280 |
| 112 and 172 | 4816 |