Least Common Multiple (LCM) of 156 and 97
The least common multiple (LCM) of 156 and 97 is 15132.
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 156 and 97?
First, calculate the GCD of 156 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 97 = 1 remainder 59 |
| 2 | 97 ÷ 59 = 1 remainder 38 |
| 3 | 59 ÷ 38 = 1 remainder 21 |
| 4 | 38 ÷ 21 = 1 remainder 17 |
| 5 | 21 ÷ 17 = 1 remainder 4 |
| 6 | 17 ÷ 4 = 4 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 72 | 2664 |
| 20 and 42 | 420 |
| 77 and 198 | 1386 |
| 74 and 51 | 3774 |
| 77 and 125 | 9625 |