In finding the HCF of two positive integers by the division method, the last divisor is 31 and the quotients, in order, are 1, 1, 5 and 2. What is the LCM of 279 and the greater of the two numbers?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2232
In the division method, each step uses dividend \(=\) divisor \(\times\) quotient \(+\) remainder, and each divisor becomes the next dividend. Starting from the last step, where 31 leaves no remainder, the two numbers can be rebuilt backwards.
Last step (quotient 2, remainder 0): dividend \(=31\times2=62\)
Third step (quotient 5, remainder 31): dividend \(=62\times5+31=341\)
Second step (quotient 1, remainder 62): dividend \(=341\times1+62=403\)
First step (quotient 1, remainder 341): dividend \(=403\times1+341=744\)
The numbers are 744 and 403; the greater is 744
\(279=3^{2}\times31\) and \(744=2^{3}\times3\times31\)
LCM \(=2^{3}\times3^{2}\times31=2232\)
The LCM of 279 and 744 is 2232.