Question

Find the length of the longest tape which can exactly measure the dimensions of
the room that has length 13.60 m, breadth 12.40 m and height 5.60 m.
​

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Length , Breadth & Height of Room are given as : 13.60m , 12.40m and 5.60m.

Now, We need to find the greatest possible length of tape which can exactly measure the dimensions of the room .

So, to find the greatest possible length of tape we need to find the H.C.F. of the given Dimensions of the room.

⇒ H.C.F. of (13.60 , 12.40 , 5.60) = H.C.F. of [ (136/10) , (124/10) , (56/10) ] = (HCF of Numerators) / (LCM of Denominators) = (HCF of 136, 124, 56) / (LCM of 10,10,10) .

Prime Factors of 136, 124 & 56 is :-

→ 136 = 2 * 2 * 2 * 17

→ 124 = 2 * 2 * 31

→ 56 = 2 * 2 * 2 * 7

HCF = 2 * 2 = 4 .

And,

→ LCM of (10,10,10) = 10 .

Therefore,

→ HCF of (13.60 , 12.40 , 5.60) = (4/10) = 0.4m. (Ans.)

Hence, Therefore, we need 0.4m longest tape to measure the three dimensions of the room.