Number systems — LCM, HCF, divisibility | LCM HCF number system JKSSB | Lemma

Lemma/JKSSB Finance Accounts Assistant/Quantitative Reasoning

JKSSB Finance Accounts Assistant · Quantitative Reasoning

Number systems — LCM, HCF, divisibility

Prime factorisation, LCM/HCF shortcuts, and divisibility rules for FAA MCQs.

Skills in this lesson

1. LCM and HCF via prime factors0/2 verified
2. Divisibility rules (2, 3, 5, 9, 11)Locked

Prerequisites

Recommended before this lesson — you can still read and practice below:

Ratio and proportion (locked)

Teach

Number-system MCQs test factorisation speed and divisibility shortcuts — not long division. Master LCM/HCF first; divisibility rules eliminate options fast.

LCM and HCF

HCF (Highest Common Factor) — largest number dividing both integers.
LCM (Least Common Multiple) — smallest number both integers divide into.

Prime factor method:

Factor each number: $12 = 2^2 \times 3$ , $18 = 2 \times 3^2$ .

18 = 2 \times 3^{2}

HCF — take the lowest power of each common prime:

2 \times 3 = 6

LCM — take the highest power of each prime present:

2^2 \times 3^2 = 36

Check: $\text{HCF} \times \text{LCM} = 12 \times 18 = 216$ , and $6 \times 36 = 216$ ✓

Divisibility rules (high yield)

| Divisor | Rule | |---------|------| | 2 | Last digit even | | 3 | Sum of digits divisible by 3 | | 5 | Last digit 0 or 5 | | 9 | Sum of digits divisible by 9 | | 11 | Alternating sum of digits divisible by 11 |

Exam discipline

JKSSB Quant is only 10 marks — one wild guess (−0.25) costs 2.5% of the full paper. Use divisibility to narrow to two options before guessing.

Practice

FAA exam rules: −0.25 marks per wrong MCQ. Blank is better than a wild guess.

Practice 1

$HCF of 12 and 18 is:$

36362

Practice 2

$LCM of 12 and 18 is:$

6243672

Practice 3

$HCF of 24 and 36 is:$

612724

Practice 4

$Which number is divisible by 9?$

234245256278

Hint

Sum of digits: 2+3+4 = 9.

Practice 5

$Which number is divisible by 11?$

121124133145

Hint

Alternating sum for 121: 1 − 2 + 1 = 0.

Practice 6

$Which number is divisible by both 2 and 5?$

125130135142

Mastery checks

Pass each skill by answering correctly on 2 of 3 checks (fewer if fewer are available). Practice questions above are rehearsal — only mastery checks count toward progress. Retry wrong answers until you succeed.

Wrong answers show the FAA −0.25 penalty as a reminder — mastery still allows retries.

LCM and HCF via prime factors

0/2 verified

Check 1

$LCM of 8 and 12 is:$

4244896

Check 2

$HCF of 15 and 25 is:$

3575125

Check 3

$For 12 and 18, HCF \times LCM equals:$

36108216324

Divisibility rules (2, 3, 5, 9, 11)

Locked — complete prior skills first

Check 1(Complete prior skills first)

$Which number is divisible by 3 but not by 9?$

123126135144

Hint

123: digit sum 6 → divisible by 3, not by 9.

Check 2(Complete prior skills first)

$The smallest 3-digit number divisible by 11 is:$

100101110111

Check 3(Complete prior skills first)

$Which is divisible by 5?$

202305412503

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