Let a and b be integers. A common multiple of a and b is an integer n for which a|n and b|n. We call an integer m the least common multiple of n provided (1) m is positive, (2) m is a common multiple of a and b, and (3) if n is any other positive common multiple of a and b, then n [greater than or equal to] m.

The notation for the least common multiple of a and b is lcm(a,b). For example, lcm(24,30)=120.

Please do the following:

(a) Develop a formula for the least common multiple of two positive integers in terms of their prime factorizations; your formula should be similar to the in Theorem 36.5

(b) Use your formula to show: If a and b are positive integers, then
ab=gcd(a,b)lcm(a,b).

... Find the least common multiple of 10, 15, and 25. A) 150 B) 3,750 C) 50 D) 30 Add. ... Add. Find the least common multiple of 48 and 96. Divide. ...

... 6. Add. 8/21 + 3/14 8. Find the least common multiple of 3, 6, and 9. 9. If 1 gallon (gal) of water weighs 8.34 pounds (lb), how much does 3.75 gal weigh? 10. ...

... With this scenario, she would need to fill up at least once a week for ... By using money as a common denominator, an individual is able to look at all factors and ...

... Find the least common multiple (LCM) for each of the following groups of numbers. Use whichever method you wish. 22. 12, 20, and 35. Add. 36. 1/3 + 5/12 + 4/5. ...

... must obtain permission from at least three other ...Common Stock Dividends Distributable is classified as a ... The solution has answers to multiple choice questions ...

45 Multiple Choice Problems Regarding Accounting issues. ... D. net sales by average common shares outstanding. ... of the following is the least likely consideration ...

Accounting: 41 Multiple choice questions. ... 2008 Retained Earnings $2,000,000 $ 1,300,000 Common Stock $ 500,000 ... remain financially viable for at least the next ...

Multiple Choice Questions in finance: cost of capital, cost of ... and Moore has 10,000 shares of common stock outstanding ... and C. Division A has the least risk and ...

... 1.) x - x = 5 2 3 First we get the LCD( least common denominator) of 2 and 3 which is 2*3=6 Therefore we multiply first fraction by 3 and second by 4 and get: ...