| Hint: Find out prime factorization of 36, 48 and 60. Find the common factors in prime factorization of 36, 48 and 60. Complete step-by-step answer:
The product of all of their prime factors will be HCF, To find the LCM, find the product of HCF and all the remaining prime factors of 36, 48 and 60. We have to find HCF and LCM of 36, 48 and 60 by prime factorization method.
Let us first find out prime factorization of 36, 48 and 60. One by one.
Prime factorization of 36,
\[\begin{align}
& 2\left| \!{\underline {\,
36 \,}} \right. \\
& 2\left| \!{\underline {\,
18 \,}} \right. \\
& 3\left| \!{\underline {\,
9 \,}} \right. \\
& 3\left| \!{\underline {\,
3 \,}} \right. \\
& \text{ }1 \\
\end{align}\]
$\Rightarrow 36=2\times 2\times 3\times 3$
Prime factorization of 48,
$\begin{align}
& 2\left| \!{\underline {\,
48 \,}} \right. \\
& 2\left| \!{\underline {\,
24 \,}} \right. \\
& 2\left| \!{\underline {\,
12 \,}} \right. \\
& 2\left| \!{\underline {\,
6 \,}} \right. \\
& 3\left| \!{\underline {\,
3 \,}} \right. \\
& \text{ 1} \\
& \Rightarrow \text{48=2}\times \text{2}\times \text{2}\times \text{2}\times \text{3} \\
\end{align}$
Prime factorization of 60.
$\begin{align}
& 2\left| \!{\underline {\,
60 \,}} \right. \\
& 2\left| \!{\underline {\,
30 \,}} \right. \\
& 3\left| \!{\underline {\,
15 \,}} \right. \\
& 5\left| \!{\underline {\,
5 \,}} \right. \\
& \text{ 1} \\
& \Rightarrow \text{60=2}\times \text{2}\times \text{3}\times \text{5} \\
\end{align}$
We have got,
$\begin{align}
& 36=2\times 2\times 3\times 3 \\
& 48=2\times 2\times 2\times 2\times 3 \\
& 60=2\times 2\times 3\times 5 \\
\end{align}$
Let us first find out the HCF of 36, 48 and 60.
To find the HCF of three numbers, we have to find the factors which one common in all three and HCF will be the product of all common factors of these three numbers
$\begin{align}
& 36=2\times 2\times 3\times 3 \\
& 48=2\times 2\times 2\times 2\times 3 \\
& 60=2\times 2\times 3\times 5 \\
\end{align}$
HCF$=2\times 2\times 3$ . Because 2,2 and 3 are the common factors in all three numbers 36, 48 and 60
$\Rightarrow HCF=12$
So, the HCF of 36, 48 and 60 is 12.
Now, let us find out LCM of 36, 48 and 60. To find the LCM, we multiply HCF with the remaining factors which are not common. We can see above that 3,2,2 and 5 are remaining. So, $LCM=HCF\times \left( 3\times 2\times 2\times 5 \right)$
$\begin{align}
& \Rightarrow LCM=12\times 3\times 2\times 2\times 5 \\
& \Rightarrow LCM=720 \\
\end{align}$
Hence LCM and HCF of 36, 48 and 60 are 720 and 12 respectively. Note: Another method to find LCM of 36, 48 and 60,
$\begin{align}
& 2\left| \!{\underline {\,
36,48,60 \,}} \right. \\
& 2\left| \!{\underline {\,
18,24,30 \,}} \right. \\
& 3\left| \!{\underline {\,
9,12,15 \,}} \right. \\
& \text{ }\left| \!{\underline {\,
3,4,5 \,}} \right. \\
& LCM=2\times 2\times 3\times 3\times 4\times 5 \\
& =720 \\
\end{align}$ We will now calculate the prime factors of 48 and 60, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48 and 60. GCF Calculatorand
and Calculate GCFHow to find the GCF of 48 and 60?We will first find the prime factorization of 48 and 60. After we will calculate the factors of 48 and 60 and find the biggest common factor number . Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor. Least common multiple (LCM) of 48 and 60 is 240. LCM(48,60) = 240 LCM Calculatorand
and Calculate LCMThe formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48 and 60, than apply into the LCM equation. GCF(48,60) = 12
LCM(48,60) = ( 48 × 60) / 12
LCM(48,60) = 2880 / 12
LCM(48,60) = 240 Least Common Multiple (LCM) of 48 and 60 with PrimesLeast common multiple can be found by multiplying the highest exponent prime factors of 48 and 60. First we will calculate the prime factors of 48 and 60.
What is the HCF for 48 and 60?
Therefore, the greatest common factor of 48 and 60 is 12.
What is the LCM of 48 and 60?
Answer: LCM of 48 and 60 is 240.
What are the HCF of 48?
HCF of 36 and 48 by Listing the Factors
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 6 common factors of 36 and 48, i.e. 1, 2, 3, 4, 6 and 12. Therefore, the highest common factor of 36 and 48 is 12.
What is the HCF and LCM of 45 and 60?
LCM of 45 and 60 is 180. The value divisible evenly by 45 and 60 gives the LCM value. Least common multiples of 45 and 60 can be found from the multiples which are common. (45, 90, 135, 180, 225, 270, ….)
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