CBSE 2025 · Region 3 · Set 1 · Q23 · 2 marks
Find the smallest number which is divisible by both $\displaystyle 644$ and 462.Two numbers are in the ratio $\displaystyle 4$ : $\displaystyle 5$ and their HCF is 11. Find the LCM of these numbers.
Find the smallest number which is divisible by both $\displaystyle 644$ and 462.
Two numbers are in the ratio $\displaystyle 4$ : $\displaystyle 5$ and their HCF is 11. Find the LCM of these numbers.
Marking-scheme solution
\[\begin{aligned}
& 462=2 \times 3 \times 7 \times 11 \\
& 644=2^{2} \times 7 \times 23 \\
& \operatorname{LCM}(462,644)=2^{2} \times 3 \times 7 \times 11 \times 23=21252
\end{aligned}
\]
\(\displaystyle \therefore\) Smallest number which is divisible by both $\displaystyle 462$ and $\displaystyle 644$ is $\displaystyle 21252$
Let the two numbers be 4x and 5x where x is common factor
Now HCF = $\displaystyle 11$
\[\therefore \mathrm{x}=11
\]
Numbers are $\displaystyle 44$ and $\displaystyle 55$
\[\operatorname{LCM}(44,55)=\frac{44 \times 55}{11}=220
\]
Real NumbersHCF and LCM by Prime FactorisationApplyvery_short_answereasy
More from Real Numbers
- (1+√3)^2-(1-√3)^2 is:2025 · asked 3×
- If x is the LCM of 4,6, 8 and y is the LCM of 3,5, 7 and p is the LCM of x and y, then which of the following…2025 · asked 3×
- Prove that √3 is an irrational number. OR State true or false for each of the following statements and…2025 · asked 3×
- √0.4 is a/an2025 · asked 3×
- (√3+2)^2+(√3-2)^2 is a/an2025 · asked 3×
- Prove that √5 is an irrational number. OR Let p, q and r be three distinct prime numbers. Check whether p · q…2025 · asked 3×
- Prove that √2 is an irrational number. OR Let x and y be two distinct prime numbers and p=x^2 y^3, q=x y^4,…2025 · asked 3×
- Prove that √3 is an irrational number.2025 · asked 3×
CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.