if LCM of lcm of two numbers a and b is 24 and their HCF is 1 then find the numbers
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3
We can get only the product of the 2 numbers from their LCM & HCF. Let me illustrate with example . Let two numbers are 4 & 10. Their HCF & LCM are 2 and 20 respectively. Forget about 4 and 10.
Product of LCM and HCF here is 2*20=40. We can write :
40 =1*40
40=2*20
40=4*10
40=5*8, Now if we zoom on the products pairs — pairs (1,40) & (5,8) can be ignored because their LCM and HCF are different than those given.But for the pair (2,20) and (4,10) in both the cases LCM and HCF are 20 and 2 which matches with the LCM and HCF of the numbers we have taken.we have taken for example two numbers 4 and 10. But from only given LCM and HCF we get more than one pair of numbers. So from only HCF and LCM we can't ascertain the exact pair.
Product of LCM and HCF here is 2*20=40. We can write :
40 =1*40
40=2*20
40=4*10
40=5*8, Now if we zoom on the products pairs — pairs (1,40) & (5,8) can be ignored because their LCM and HCF are different than those given.But for the pair (2,20) and (4,10) in both the cases LCM and HCF are 20 and 2 which matches with the LCM and HCF of the numbers we have taken.we have taken for example two numbers 4 and 10. But from only given LCM and HCF we get more than one pair of numbers. So from only HCF and LCM we can't ascertain the exact pair.
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4
Answer:
Given
LCM=24
HCF=1
HCF×LCM=a×b
24×1=a×b
Factors of 24 are
(2,12),(1,24),(3,8),(4,6)
Therefore the given situation tally to (1,24) and the numbers are 1,24
Step-by-step explanation:
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