Prime Factors, HCF & LCM Quiz

1. What is the prime factorisation of 60?

• A. $2^{2} \times 3 \times 5$
• B. $2 \times 3^{2} \times 5$
• C. $2^{2} \times 5 \times 3^{2}$
• D. $2 \times 3 \times 5^{2}$

2. Which method is used to find the HCF from two prime factorisations?

• A. Add the powers of each common prime
• B. Take the highest power of every prime present
• C. Take the lowest power of each prime common to both numbers
• D. Multiply all the primes listed regardless of power

3. Given $48 = 2^{4} \times 3$ and $180 = 2^{2} \times 3^{2} \times 5$, what is the HCF?

• A. $2^{2} \times 3 = 12$
• B. $2^{4} \times 3^{2} \times 5 = 720$
• C. $2 \times 3 = 6$
• D. $2^{2} \times 3^{2} = 36$

4. Given $48 = 2^{4} \times 3$ and $180 = 2^{2} \times 3^{2} \times 5$, what is the LCM?

• A. $2^{4} \times 3^{2} \times 5 = 720$
• B. $2^{2} \times 3 \times 5 = 60$
• C. $2^{4} \times 3^{2} = 144$
• D. $2^{2} \times 3^{2} \times 5 = 180$

5. Two warning lights flash every 18 seconds and every 24 seconds respectively, both flashing together at $t=0$. Using the HCF/LCM relationship, after how many seconds will they next flash together, given $\text{HCF}(18,24)=6$?

• A. $18 \times 24 \div 6 = 72$ seconds
• B. $18 \times 24 \times 6 = 2592$ seconds
• C. $18 + 24 - 6 = 36$ seconds
• D. $6$ seconds