SSC CGL 2025 Tier-I · 18 September 2025, Shift 2 · General Intelligence and Reasoning · Question 20 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

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Find the LCM of 12, 18, 30?

(a)90
(b)180
(c)60
(d)120

Answer

Why

Correct — B.
Rule: take each prime at the highest power it reaches in any of the numbers.

12 = 2² × 3
18 = 2 × 3²
30 = 2 × 3 × 5

Highest powers: 2², 3², 5
LCM = 4 × 9 × 5 = 180
Check: 180 ÷ 12 = 15, 180 ÷ 18 = 10, 180 ÷ 30 = 6 → option (b).

Why the others are wrong

(a)
90 — 90 = 2 × 3² × 5 has a single factor of 2, but 12 needs 2². 90 ÷ 12 = 7.5, so 90 is not a multiple of 12.
(c)
60 — 60 = 2² × 3 × 5 has a single factor of 3, but 18 needs 3². 60 ÷ 18 is not a whole number.
(d)
120 — 120 = 2³ × 3 × 5 carries a spare 2 and still a single 3. 120 ÷ 18 is not a whole number, so it misses 18.

Concept

The LCM (least common multiple) is the smallest number that each of the given numbers divides exactly. Break each number into primes, then take each prime at the highest power it reaches in any one number.

Here 2 peaks at 2² (from 12), 3 at 3² (from 18) and 5 at 5¹ (from 30). Multiply them: 4 × 9 × 5 = 180.

A quick filter: the LCM must be a multiple of the largest number, 30. All four options (90, 180, 60, 120) pass that test, so 12 and 18 have to be checked too.

Key facts

LCM takes the highest power of each prime, HCF the lowest power of each shared prime.
12 = 2² × 3, 18 = 2 × 3², 30 = 2 × 3 × 5.
The HCF of 12, 18 and 30 is 2 × 3 = 6.
HCF × LCM equals the product for two numbers, but not in general for three: here 6 × 180 = 1,080, while 12 × 18 × 30 = 6,480.

Study next

HCF of several numbers by prime factorisationLeast number that leaves the same remainder when divided by 12, 18 and 30LCM and HCF of fractions

Common traps

Stopping at a common multiple of two of the numbers: 60 is a multiple of 12 and 30 but not of 18
Taking the lowest power of each prime, which gives the HCF (6), not the LCM
Multiplying 12 × 18 × 30 = 6,480, which is a common multiple but not the least

Here it is set as a bare three-number LCM in the Reasoning section, with all four options multiples of 30, so the largest number alone cannot decide it.

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