Tag: lowest common multiple (l.c.m.)

Questions Related to lowest common multiple (l.c.m.)

Solve the given exponent:
$\sqrt[4]{12} \times \sqrt[7]{6}$  

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

  1. $2^{\frac{9}{14}}\times 3^{\frac{11}{28}}$

  2. $3^{\frac{9}{14}}\times 2^{\frac{11}{28}}$

  3. $2^{\frac{1}{14}}\times 3^{\frac{1}{28}}$

  4. $3^{\frac{1}{14}}\times 2^{\frac{1}{28}}$

Show answer
Correct Option: A
Explanation:

$\sqrt[4]{12} \ \times \ \sqrt[7]{6}$


$=(12)^{\frac{1}{4}} \ \times \ (6)^{\frac{1}{7}}$

$=(2\times2\times3)^{\frac{1}{4}} \ \times \ (2\times3)^{\frac{1}{7}}$

$=(2^2\times3)^{\frac{1}{4}} \ \times \ (2\times3)^{\frac{1}{7}}$

$=2^{2\times(\frac{1}{4})}\times 3^{\frac{1}{4}} \ \times2^\frac{1}{7}\times3^\frac{1}{7}$

$=2^{\frac{1}{2}}\times 3^{\frac{1}{4}} \ \times2^\frac{1}{7}\times3^\frac{1}{7}$

$=2^{(\frac{1}{2}+\frac{1}{7})}\times 3^{(\frac{1}{4}+\frac{1}{7})}$-----If base is same, then their powers can be added, by product law.

$=2^{\frac{9}{14}}\times 3^{\frac{11}{28}}$

Option A.

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.

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

  1. $7:27:30$ hours

  2. $7:28:00$ hours

  3. $7:27:50$ hours

  4. $7:27:45$ hours

Show answer
Correct Option: D
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.

State true or false:

The common factors of $18$ and $24$ are $1,2,3,6$.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Factors of $ 18 = 1, 2, 3, 6, 8, 9$ and $ 18 $

Factors of $ 24 = 1, 2, 3, 4, 6, 8, 12 $ and $ 24 $

Common factors are $ 1, 2, 3, 6 $

State the following statement is True or False
The common factors of $75$ and $50$ are $1,5,25$
maths be my multiple, i'll be your factor co-prime numbers lcm lowest common multiple (l.c.m.)

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Factors of $ 50 = 1, 2, 5, 10, 25 $ and $ 50 $

Factors of $ 75 = 1,3, 5, 15, 25 $ and $ 75 $

Common factors are $ 1, 5, 25 $

Common factors of $9$ and $36$ are 

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

  1. $1,3,9$

  2. $1,4,3,5,9$

  3. $1,4,5$

  4. None 

Show answer
Correct Option: A
Explanation:

Factors of $ 9 $  are $ 1, 3, 9 $
Factors of $ 36 $ are $ 1, 3, 4, 6, 9, 12, 36 $
$\therefore $ common factors are $ 1, 3, 9 $.

In a school, $351$ boys and $273$ girls have been divided into the largest possible equal classes with each class having equal boys and girls. Find the number of classes

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

  1. $11$

  2. $13$

  3. $10$

  4. $9$

Show answer
Correct Option: B

What is the least number by which 2352 is to be multiplied to make it a perfect square?

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

  1. $6$

  2. $4$

  3. $3$

  4. $8$

Show answer
Correct Option: C
Explanation:
$2$ $2352$
$2$ $1176$
$2$ $588$
$2$ $294$
$3$ $147$
$7$ $49$
$7$

L.C.M of $2352=2^2\times 2^2\times 7^2\times 3$
To make $2352$ a perfect square it must be multiplied by $3$

Find the 1st common multiple of $6$ and $8$.

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

  1. $24$

  2. $16$

  3. $12$

  4. $2$

Show answer
Correct Option: A
Explanation:

$1$st common multiple of $6,8$ is same as LCM of these numbers.


$6 = 2\times3$
$8 = 2^{3}$

$\therefore$ LCM $= 2^{3}\times3 = 24$

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

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

  1. $10,20,30,40$

  2. $120,240,360,480$

  3. $8,40,80,120$

  4. $6,60,120,240$

Show answer
Correct Option: B
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 $= 120,240,360,480$

Find two common multiples of $12,15$

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

  1. $48,96$

  2. $60,120$

  3. $10,20$

  4. $24,30$

Show answer
Correct Option: B
Explanation:

$12= 2^{2}\times 3$

$15 = 3\times5$

$\Rightarrow$ LCM$= 2^{2}\times3\times5 = 60$

$\therefore 60$ is the least common multiple of $12,15$. Thus, all multiples of $60$ are common multiples of $12$ and $15$.

Answer $= 60,120$