7. (a) The product of two number is 6656 and their LCM is 256. Find their HCF.
(b) Find the greatest 4-digit number that is exactly divisible by 6, 15, and 18.
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Step-by-step explanation:
(a).
Product of 2 numbers = Product of their LCM and HCF
ab = LCM × HCF
6656 = 256 × HCF
6656/265 = HCF
HCF = 26
(b).
Basically what we need now is the LCM of 6, 15, 18
6 = 2*3
15 = 3*5
18 = 2*3²
LCM - 2*3²*5 = 90
Greatest 4 digit no. is 9999
9999 = 90 × 111 + 9
9999 - 9 = 90 × 111
9990 = 90 × 111
So the greatest 4 digit which is divisible by 6, 15 and 18 is 9990.
I hope it will help you.
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