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- Q102761-f22ea70b-4f88-0f5f-04c5-8725efaf6536 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle a,b,h'\in \mathbb {Z} \land (a\neq 0\lor b\neq 0)\land h\in \mathbb {N} \implies \operatorname {lcm} (a,b)=\{h:(a\mid h\land b\mid h)\land (a\mid h'\land b\mid h'\implies h\mid h')\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <msup> <mi>h</mi> <mo>′</mo> </msup> <mo>∈<!-- ∈ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo>∧<!-- ∧ --></mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>≠<!-- ≠ --></mo> <mn>0</mn> <mo>∨<!-- ∨ --></mo> <mi>b</mi> <mo>≠<!-- ≠ --></mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>∧<!-- ∧ --></mo> <mi>h</mi> <mo>∈<!-- ∈ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mspace width="thickmathspace" /> <mo stretchy="false">⟹<!-- ⟹ --></mo> <mspace width="thickmathspace" /> <mi>lcm</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <mi>h</mi> <mo>:</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>∣<!-- ∣ --></mo> <mi>h</mi> <mo>∧<!-- ∧ --></mo> <mi>b</mi> <mo>∣<!-- ∣ --></mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>∧<!-- ∧ --></mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>∣<!-- ∣ --></mo> <msup> <mi>h</mi> <mo>′</mo> </msup> <mo>∧<!-- ∧ --></mo> <mi>b</mi> <mo>∣<!-- ∣ --></mo> <msup> <mi>h</mi> <mo>′</mo> </msup> <mspace width="thickmathspace" /> <mo stretchy="false">⟹<!-- ⟹ --></mo> <mspace width="thickmathspace" /> <mi>h</mi> <mo>∣<!-- ∣ --></mo> <msup> <mi>h</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a,b,h'\in \mathbb {Z} \land (a\neq 0\lor b\neq 0)\land h\in \mathbb {N} \implies \operatorname {lcm} (a,b)=\{h:(a\mid h\land b\mid h)\land (a\mid h'\land b\mid h'\implies h\mid h')\}}</annotation> </semantics> </math>" @default.