Tag: lcm

Questions Related to lcm

What is the least common multiple of $10$ and $20$?

maths hcf-lcm introduction to multiples multiples lcm

  1. $2$

  2. $5$

  3. $10$

  4. $20$

  5. $200$

Show answer
Correct Option: D
Explanation:

$10=2\times5$
$20=2^2\times 5$

LCM$=2\times2 \times 5=20$
Ans-Option $D$.

The greatest number with four digits which when divided by $3, 5, 7, 9$ leaves the remainders $1, 3, 5, 7$ respectively, is _______.

maths hcf-lcm introduction to multiples multiples lcm

  1. $9763$

  2. $9673$

  3. $9367$

  4. $9969$

Show answer
Correct Option: A
Explanation:

Since on dividing by $3$ the remainder is $1$, the sum of digits of the number must add upto a number, dividing which by $3$ we get remainder $1$

Since on dividing by $5$ remainder is $3$, unit place digit has to be either $3$ or $8$
Since on dividing by $9$ remainder is $7$, sum of digits should give remainder $7$ when divided by $9$ 
Only options (A), (B) satisfy these criteria
Since (A) is bigger, we divide it by $7$ and find remainder which turns out to be $5$. 

When $31513$ ad $34369$ are divided by a certain three digit number, the remainders are equal, then the remainder is ______.

maths hcf-lcm introduction to multiples multiples lcm

  1. $86$

  2. $97$

  3. $374$

  4. $113$

Show answer
Correct Option: B
Explanation:

Let the divisor be $a$ and remainder be $r$

Let $31513 = am+r$
and $34369 = an+r$
Then, $a(n-m) = 2856 = 24\times119 = 12\times238 = 8\times357= 6\times476=4\times714$
All three digit numbers give same remainder $=$ $97$

The numbers which are multiples of $2$ are called ____.

maths hcf-lcm introduction to multiples multiples lcm

  1. odd

  2. even

  3. prime

  4. composite

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Correct Option: B
Explanation:

The numbers $2,4,6,8,10$ are known as even number. 

The numbers which are completely divisible by $2$ are known as even numbers.
So, the numbers which are multiples of $2$ are called even numbers.

LCM of numbers 1, 2, 3 is equal to their

maths hcf-lcm introduction to multiples multiples lcm

  1. product

  2. division

  3. sum

  4. difference

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Correct Option: A,C
Explanation:

$2, 3$ are primes.
$\therefore$ Each number has no factor other than $1$ and itself.
$\therefore$ Their LCM is the product of the numbers.
$\therefore$ LCM of $1,2,3=2\times 3=6$.
Also here $1+2+3=6$.
Answer- Option A and Option C.

L.C.M. of two co-prime numbers is their

maths hcf-lcm introduction to multiples multiples lcm

  1. sum

  2. difference

  3. product

  4. quotient

Show answer
Correct Option: C
Explanation:

The two numbers which have only 1 as their common factor are called co-primes.

For example, Factors of $ 5 $  are $ 1, 5 $
Factors of $ 3 $ are $ 1, 3 $

Common factors is $ 1 $.
So they are co-prime numbers.

To find their LCM, we

then choose each prime number with the greatest power and multiply them to get the LCM.
$ => LCM = 3 \times 5 = 15 $

Hence, LCM of two co-prime numbers is their product.

What are the three common multiples of $18$ and $6$?

maths hcf-lcm introduction to multiples multiples lcm

  1. $18, 6, 9$

  2. $18,36,6$

  3. $36, 54, 72$

  4. none of these

Show answer
Correct Option: C
Explanation:

Multiples of $ 18 = 18, 36, 54, 72..... $

Multiples of $ 6 = 6, 12, 18, 24.... $
The first common multiple will be $ 18 $

And the next common multiples will be multiples of $ 18 $
Hence, the common multiples of $ 18, 6 $ are $ 18, 36, 54, 72 $...

Bhushan counted to $60$ using multiples of $6.$ Which statement is true about multiples of $6?$

maths hcf-lcm introduction to multiples multiples lcm

  1. They are all odd numbers.

  2. They all have $6$ in the ones place.

  3. They can all be divided evenly by $3.$

  4. They can all be divided evenly by $12.$

Show answer
Correct Option: C
Explanation:

Multiple of $6$ like $6, 12, 18,24,30$ and they can all be divided evenly by $3$.
So option $C$ is correct.

Every number is a ...... and a ........ of itself.

maths hcf-lcm introduction to multiples multiples lcm

  1. factor, multiple

  2. prime, composite

  3. even, odd

  4. none of these

Show answer
Correct Option: A
Explanation:

Every number is a factor and a multiple of itself. 

For example, $ 10 $ has a factor $ 10 $ as well as a multiple $ 10. $

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 of these

Show answer
Correct Option: A
Explanation:

Factors of $ 9 = 1, 3, 9 $
Factors of $ 36 = 1, 3, 4, 6, 9, 12, 36 $

Common factors are $ 1, 3, 9 $