Least Common Multiple (LCM) of 97 and 156
The least common multiple (LCM) of 97 and 156 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 97 and 156?
First, calculate the GCD of 97 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 156 = 0 remainder 97 |
| 2 | 156 ÷ 97 = 1 remainder 59 |
| 3 | 97 ÷ 59 = 1 remainder 38 |
| 4 | 59 ÷ 38 = 1 remainder 21 |
| 5 | 38 ÷ 21 = 1 remainder 17 |
| 6 | 21 ÷ 17 = 1 remainder 4 |
| 7 | 17 ÷ 4 = 4 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 60 | 1740 |
| 53 and 27 | 1431 |
| 70 and 16 | 560 |
| 63 and 33 | 693 |
| 60 and 27 | 540 |