Tag: lcm

Quizzes (0) Questions (53)

Questions Related to lcm

Multiple choice maths be my multiple, i'll be your factor co-prime numbers lcm lowest common multiple (l.c.m.)

Choose the most appropriate option.
The traffic lights at three different signal points change after every $45$ seconds, $75$ seconds and $90$ seconds respectively. If all change simultaneously at $7:20:15$ hours, then they will change again simultaneoulsy at.

  1. $7:27:30$ hours
  2. $7:28:00$ hours
  3. $7:27:50$ hours
  4. $7:27:45$ hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
The $3$ signals (at $3$ points) change every $45 s,\, 75 s,\, 90 s$

So, they will change simultaneously for a common time, which is the common multiple or $L.C.M$ of the three

$\Rightarrow$  $45 = 5\times 9 = 3^2 \times 5$ 

$\Rightarrow$  $75 = 3\times 25 = 3\times 5^2$

$\Rightarrow$  $90 = 9\times 10 = 2\times 3^2\times 5$

$L.C.M= 2 \times 3^2 \times 5^2 = 2\times 9\times 25 = 450s$

So, they will change simultaneously every $450s$ or $7\,mins\,30 \,sec$

$\Rightarrow$  So, next they will change together at $7:27:45$ hours.
Multiple choice maths be my multiple, i'll be your factor co-prime numbers lcm lowest common multiple (l.c.m.)

the first four common multiple of numbers $6,8,10$ are

  1. $10,20,30,40$
  2. $120,240,360,480$
  3. $8,40,80,120$
  4. $6,60,120,240$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$6 = 2\times3$
$8 = 2^{3}$
$10 = 2\times5$

$\Rightarrow$ LCM of $6,8,10 = 2^{3}\times3\times5 = 120$

$\therefore 120$ is the least common multiple of $6,8,10$. Thus, all multiples of $120$ are common multiples of $6,8$ and $10$.

$\therefore$ First four common multiples $= 120,240,360,480$
Multiple choice maths be my multiple, i'll be your factor co-prime numbers lcm lowest common multiple (l.c.m.)

The 1st three common multiple of numbers $12,8,16 $ are

  1. $12,24,36$
  2. $8,16,24$
  3. $16,32,48$
  4. $48,96,144$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$12 = 2^{2}\times3$
$8 = 2^{3}$
$16 = 2^{4}$

$\Rightarrow$ LCM of $12,8,16 = 2^{4}\times3 = 48$

$\therefore 48$ is the least common multiple of $12,8,16$. Thus, all multiples of $48$ are common multiples of $12,8$ and $16$.

$\therefore$ First three common multiples $= 48,96,144$