Question

three measurement rodes 64cm,80cm,and 96cm are long respectively. by using any rodes, which least length of cloth can be fully measured?

Answer 1

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THANKYOU YOU ASKING
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ΦLengths of three measuring rods
= 64 cm, 80 cm, 96 cm

ΦLeast length of the cloth that can be measured
= LCM of 64, 80 and 96

LCM of 64, 80 and 96 = 960

Number of times that the rod of length 64 cm has to be used
= 960/64 = 15

Number of times that the rod of length 80 cm has to be used
= 960/80 = 12

Number of times that the rod of length 96 cm has to be used
= 960/96 = 10

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Answer 2

Hey friend ☺
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For measuring least length of cloth by these measures tapes we need to find the LCM of these measurements
so I'm gonna use class 10 method
by using Euclid division lemma

To find HCF first let's apply edl on 80 and 64
$80 = 64 \times 1 + 16 \\ 64 = 16 \times 4 + 0$
so HCF (80,64)=16

Now apply Euclid division lemma on 90 and 16
$90 = 16 \times 5 + 10 \\ 16 = 10 \times 1 + 6 \\ 10 = 6 \times 1 + 4 \\ 6 = 4 \times 1 + 2 \\ 4 = 2 \times 2 + 0$
resultant HCF (90,80,64)= 2

Now we can easily find the LCM by using
verify relationship between LCM× HCF= product of two numbers

but here numbers are three I will use some extra ordinary technique
we will apply (80,64) then will equate with other one

$lcm = \frac{80 \times 64}{16} \\ = 320$
now let's find the LCM relationship between another one

$lcm = \frac{90 \times 16}{2} \\ = 720$
So here we had included 16 twice so we need to minimise it

$720 + 320 - 16 \\ = 1024$
hope it helps you