Find the LCM & HCF for the given numbers.

Question

ScanSolve AI Tutor · Accepted Answer

Lati wa LCM (Least Common Multiple) ati HCF (Highest Common Factor) fun awọn nọmba wọnyi, a yoo lo ọna ipin nọmba akọkọ (prime factorization).

1. Fun awọn nọmba 63, 42, 21

Wa awọn ipin nọmba akọkọ fun nọmba kọọkan.
$\begin{align*} 63 &= 3 \times 3 \times 7 = 3^2 \times 7 \\ 42 &= 2 \times 3 \times 7 \\ 21 &= 3 \times 7 \end{align*}$
Wa HCF (Highest Common Factor).
Eyi ni ọja ti awọn ipin nọmba akọkọ ti o wọpọ pẹlu agbara ti o kere julọ.
$\text{HCF} = 3^1 \times 7^1 = 3 \times 7 = \boxed{\text{21}}$
Wa LCM (Least Common Multiple).
Eyi ni ọja ti gbogbo awọn ipin nọmba akọkọ ti o wa ninu awọn nọmba pẹlu agbara ti o ga julọ.
$\text{LCM} = 2^1 \times 3^2 \times 7^1 = 2 \times 9 \times 7 = \boxed{\text{126}}$
2. Fun awọn nọmba 144, 216, 360
Wa awọn ipin nọmba akọkọ fun nọmba kọọkan.
$\begin{align*} 144 &= 2 \times 2 \times 2 \times 2 \times 3 \times 3 = 2^4 \times 3^2 \\ 216 &= 2 \times 2 \times 2 \times 3 \times 3 \times 3 = 2^3 \times 3^3 \\ 360 &= 2 \times 2 \times 2 \times 3 \times 3 \times 5 = 2^3 \times 3^2 \times 5 \end{align*}$
Wa HCF.
$\text{HCF} = 2^3 \times 3^2 = 8 \times 9 = \boxed{\text{72}}$
Wa LCM.
$\text{LCM} = 2^4 \times 3^3 \times 5^1 = 16 \times 27 \times 5 = \boxed{\text{2160}}$
3. Fun awọn nọmba 280, 105, 175
Wa awọn ipin nọmba akọkọ fun nọmba kọọkan.
$\begin{align*} 280 &= 2 \times 2 \times 2 \times 5 \times 7 = 2^3 \times 5 \times 7 \\ 105 &= 3 \times 5 \times 7 \\ 175 &= 5 \times 5 \times 7 = 5^2 \times 7 \end{align*}$
Wa HCF.
$\text{HCF} = 5^1 \times 7^1 = 5 \times 7 = \boxed{\text{35}}$
Wa LCM.
$\text{LCM} = 2^3 \times 3^1 \times 5^2 \times 7^1 = 8 \times 3 \times 25 \times 7 = \boxed{\text{4200}}$
4. Fun awọn nọmba 126, 234, 90
Wa awọn ipin nọmba akọkọ fun nọmba kọọkan.
$\begin{align*} 126 &= 2 \times 3 \times 3 \times 7 = 2^1 \times 3^2 \times 7^1 \\ 234 &= 2 \times 3 \times 3 \times 13 = 2^1 \times 3^2 \times 13^1 \\ 90 &= 2 \times 3 \times 3 \times 5 = 2^1 \times 3^2 \times 5^1 \end{align*}$
Wa HCF.
$\text{HCF} = 2^1 \times 3^2 = 2 \times 9 = \boxed{\text{18}}$
Wa LCM.
$\text{LCM} = 2^1 \times 3^2 \times 5^1 \times 7^1 \times 13^1 = 2 \times 9 \times 5 \times 7 \times 13 = \boxed{\text{8190}}$
5. Fun awọn nọmba 160, 96, 224
Wa awọn ipin nọmba akọkọ fun nọmba kọọkan.
$\begin{align*} 160 &= 2 \times 2 \times 2 \times 2 \times 2 \times 5 = 2^5 \times 5^1 \\ 96 &= 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3^1 \\ 224 &= 2 \times 2 \times 2 \times 2 \times 2 \times 7 = 2^5 \times 7^1 \end{align*}$
Wa HCF.
$\text{HCF} = 2^5 = \boxed{\text{32}}$
Wa LCM.
$\text{LCM} = 2^5 \times 3^1 \times 5^1 \times 7^1 = 32 \times 3 \times 5 \times 7 = \boxed{\text{3360}}$

Find the LCM & HCF for the given numbers.

Step-by-step solution

Wa awọn ipin nọmba akọkọ fun nọmba kọọkan.

Wa HCF (Highest Common Factor).

Wa LCM (Least Common Multiple).

Wa awọn ipin nọmba akọkọ fun nọmba kọọkan.

Wa HCF.

Wa LCM.

Wa awọn ipin nọmba akọkọ fun nọmba kọọkan.

Wa HCF.

Wa LCM.

Wa awọn ipin nọmba akọkọ fun nọmba kọọkan.

Wa HCF.

Wa LCM.

Wa awọn ipin nọmba akọkọ fun nọmba kọọkan.

Wa HCF.

Wa LCM.

Still stuck on this one?

More Mathematics Questions