There are five numbers. HCF of each possible pair is 4 and LCM is 27720. What will be the product of all five numbers?
a. 1540876
b. 906732
c. 7096320
d. 758430
Answers
Defining the numbers
Let the numbers be 4 a , 4 b , 4 c , 4 d , 4 e
4 is the HCF of all these number.
So 4 is common in all numbers .
LCM of 5 numbers
Note that LCM will be : 4 × a × b × c × d × e ............(1)
[a , b , c , d and e are relatively primes as given in the question]
LCM is the lowest common multiple .
Only 4 is common and others are relatively primes .
Figuring out the product
Product = 4⁵ × abcde
From (1), LCM = 4 abcde
==> abcde = LCM/4 ..................(2)
Putting this in product
==> Product = LCM/4 ×4⁵
= 27720 × 4⁴
= 7096320.
Answer
OPTION C
Hope it helps u :-)
And blame my calculator if ans is wrong XD
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Answer:
7096320
Step-by-step explanation:
Let numbers be a,b,c,d,e,
5 numbers have hcf 4
product will be abcde
lcm = 27720
lcm = abcde/4^4
abcde/4^4=27720
abcde=27720*4^4
=abcde=27720*256
abcde=7096320
Hope it helps