Method of Finding LCM

Q.

Find the least number that is divisible by all the numbers between $1$ and $10$ (both inclusive).

Q.

Can two numbers have 16 as their HCF and 380 as their LCM? Give reason.

Q.

Find the largest four-digits number which when divided by 4, 7 and 13 leaves a remainder of 3 in each case.

Q.

Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

Q.

Find HCF and LCM of $336$ and $54$ by prime factorization and verify that?

Q.

Find the smallest number which when increased by $17$ is exactly divisible by $520$ and $468$.

Q.

check whether 12ⁿ cannot end with the digit 0 or 5 for any natural number n

Q.

Find the smallest number which when divided by $28$ and $32$, respectively, leaves a remainder, $8$ and $12$ respectively.

Q. If a = 2³ ✕ 3, b = 2 ✕ 3 ✕ 5, c = 3ⁿ ✕ 5 and LCM (a, b, c) = 2³ ✕ 3² ✕ 5, then n =

(a) 1
(b) 2
(c) 3
(d) 4

Q. The LCM and HCF of two rational numbers are equal, then the numbers must be

(a) prime
(b) co-prime
(c) composite
(d) equal

Q. Show that 12ⁿ cannot end with the digit 0 or 5 for any natural number n.

Q.

Find the HCF and LCM of 6, 72 and 120 using the prime factorisation method. [3 MARKS]

Q.

Check whether 15^n can end with the digit zero for any natural number n.

Q.

Find the L.C.M and H.C.F. of 1296 and 2520 by applying the fundamental theorem of arithmetic method i.e. using the prime factorisation method. [3 MARKS]

Q.

Find the HCF and LCM of$612$and $1314$by using prime factorization method.

Q. If a is an odd number, b is not divisible by 3 and LCM of a and b is p. What is the LCM of 3a and 2b ?

Q. If p and q are two prime number, then what is their LCM?

Q.

If a and b are two prime numbers then find LCM(a, b).

Q.

Determine the smallest $3$-digit number which is exactly divisible by $6,8,\mathrm{and}12$.

Q.

Find the greatest no.of 5-digits exactly divisible by 12, 15, 36.

Q.

Find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.

Q.

Can we have any n € N, for which 7^n ends with the digit zero?

Q.

Find the least multiple of $23$ which when divided by $18,21$ and $24$ leaves remainder $7,10$ and $13$ respectively

Q. The largest 4-digit number exactly divisible by 12, 15, 18 and 27 is

1. 9690
2. 9820
3. 9720
4. 9976

Q. If two positive ingeters a and b are expressible in the form a = pq² and b = p³q; p, q being prime number, then LCM (a, b) is

(a) pq
(b) p³q³
(c) p³q²
(d) p²q²

Q.

What is the difference between LCM and HCF of $20,30,40$?

Q.

Using prime factorisation, find the HCF and LCM of :

(i) 8, 9, 25 (ii) 12, 15, 21 (iii) 17, 23, 29

(iv) 24, 36, 40 (v) 30, 72, 432 (vi) 21, 28, 36, 45

Q.

Check whether 14ⁿ can end with the digit zero...for any real integer n

Q. 81. The greatest number of four digits which when divided by 3, 5, 7, 9 leaves the remainders 1, 3, 5, 7 respectively is

Q.

If $a=2^3\times 3$, $b=2\times 3\times 5$, $c=3^n\times 5$ and LCM ($a,b,c$) $=2^3\times 3^2\times 5$, then $n=$ ? (Here, $n$ is a natural number)

1. $1$
2. $2$
3. $3$
4. $4$