Question

Three measuring tapes are 64 cm., 72 cm. and 96 cm. What is the least length that can be measured by any of the tapes exactly?

Answer 1

Dear Student,

◆ Answer -

Least length that can be measured exactly = 576 cm

● Explaination -

Least length that can be measured accurately by given tapes will be lowest common multiple of individual tapes.

Lowest common multiple is calculated by -

64 = 2 × 2 × 2 × 2 × 2 × 2

72 = 2 × 2 × 2 × 3 × 3

96 = 2 × 2 × 2 × 2 × 2 × 3

LCM = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 = 576

Therefore, the least length that can be measured by any of the tapes exactly is 576 cm.

Best luck dear...

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

Three measuring tapes are 64 cm., 72 cm. and 96 cm

TO DETERMINE

The least length that can be measured by any of the tapes exactly

CALCULATION

For a tape to be measured exactly by all the given tapes, it must be a multiple of each of the lengths of the tapes .

Now, since the least length of such a tape is to calculated , we have to find the Least Common Multiple ( LCM ) of the lengths of the given three tapes.

The given three tapes are of length

64 cm, 72 cm, 96 cm

Now we are proceeding to find LCM

$64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$

$72 = 2 \times 2 \times 2 \times 3 \times 3$

$96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3$

$\sf{Hence \: \: LCM \: of \: \: 64 \: , \: 72 \: , \: 96\:}$

$\sf{= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3}$

$\sf{ = 576}$

RESULT

The least length that can be measured by any of the tapes exactly is 576 cm

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

If A and B are two whole number than which of the Following is true a+b=b+a , ab=ba , a-b=b-a

https://brainly.in/question/23325354